I don't use either method you are asking about. I use limewater in an ATO, but the choice depends a lot on the creatures you plan to keep.
I compare various ways of dosing calcium and alkalinity in this article, including cost comparisons:
The Many Methods for Supplementing Calcium and Alkalinity - REEFEDITION
from it:
Calcium Carbonate/Carbon Dioxide Reactors
Calcium carbonate/carbon dioxide reactors work by removing water from the tank, adding carbon dioxide to reduce the pH to about pH 6.5, and then allowing the more acidic water to dissolve solid calcium carbonate media that is present in a mixing chamber. The water is then returned to the tank with its extra calcium and alkalinity (bicarbonate):
CaCO3 + H+ → Ca2+ + HCO3-
Reef tanks employing such reactors typically run at a pH below that of natural seawater, with typical tank pH values of 7.7 to 8.1. The reason for the low pH is the constant delivery of low pH solution to the tank, adding both excess CO2 and bicarbonate. There is no way around this completely, but some reactors incorporate a second chamber, allowing the liquid to pass over additional calcium carbonate media, making better use of the carbon dioxide that is actually added. Aquaria then blow off this extra CO2 and the pH rises, but the effect is typically not complete, and the pH often stays below what would be the case if the same tank water were fully aerated (that is, equilibrated) with normal air.
The media used is important in these systems, with the aragonite form of calcium carbonate being more readily dissolved than the calcite form (although both work). Also, the nature of the impurities can be very important, as nearly all of the impurities will be dissolved and delivered to the tank. Some of these impurities may be desired by the aquarist (such as magnesium and strontium) and some may not be (such as phosphate or copper). Phosphate in reactor media has sometimes become a point of competition between commercial suppliers of media for such reactors, but I would advise aquarists to be skeptical of some of these claims.
One big advantage of these reactors is that they can be scaled to deliver any amount of calcium and alkalinity needed by any tank. For this reason, they are greatly favored by those who have tanks with a high demand for calcium and alkalinity. Because of the low pH that often results, many of these aquarists choose to dose limewater in conjunction with the reactor, not because the reactor cannot supply enough calcium and alkalinity, but purely to raise the pH in the tank itself. The synergy between limewater and CaCO3/CO2 reactors involves more than just pH. Limewater uses up CO2 and CaCO3/CO2 reactors deliver it to the tank. Together, they combine to keep CO2(and consequently, pH) more in line with natural seawater.
Calcium carbonate/carbon dioxide reactors take up a substantial amount of space, since one needs a carbon dioxide cylinder, a reaction chamber, and a pump. Typically, these systems are used close to a tank, but they could be remote if appropriate water flows to and from the tank could be worked out. Once an aquarist has properly adjusted the reactor system, it requires minimal monitoring for a substantial period. Tank salinity will not increase over time using calcium carbonate/carbon dioxide reactors.
The likelihood of problems from overdosing using such a reactor is minimal. Since the pH is typically low, even substantially elevated calcium and alkalinity values may not cause a dramatic calcium carbonate precipitation event. More likely is just slow precipitation onto heaters and pump impellers. Accidental delivery of large amounts of CO2 to the tank is a concern, but that is a rare accident.
The initial costs of such reactor systems can be considerable, typically about $300-600 for the reactor itself, plus additional costs for the CO2 apparatus. Media costs vary, but a bit over $2 per pounds is typical. That puts the media cost at about $0.30 per thousand meq of alkalinity. DIY ground limestone can be used as media for a tiny fraction of this cost, if you can find it locally. The carbon dioxide cost also needs to be figured in, so that might push the total to about $0.40 per thousand meq of alkalinity.
The primary safety concern for these systems involves the carbon dioxide gas cylinder. Any high-pressure gas cylinder can be very dangerous if the cylinder head should become damaged. So be careful to not drop such cylinders least they become rockets.
Two-part Balanced Additive Systems
There are now a plethora of two-part balanced systems for supplementing calcium and alkalinity, as well as DIY recipes that I have published and for which suppliers sell quality DIY ingredients. These are always liquid additives that you add equally to tanks to supplement both calcium and alkalinity. In the DIY version, magnesium is added to the aquarium as a third solution, although it need not be added especially frequently. The rational for this type of product is that the bicarbonate and carbonate that one might like to dose to supplement alkalinity are not readily compatible with the calcium that is also needed. So one portion contains calcium and the other contains the alkalinity. When a DIY is used, the magnesium sulfate in it is not compatible with either part, so it needs its own solution.
In the simplest form, such a system would be provided by any calcium salt at one concentration in one bottle, and a carbonate alkalinity supplement in the other bottle. Within that constraint, manufacturers have a fair amount of room to play. Typically these additives claim go a step further. When the calcium and alkalinity are taken out of the picture, as they will be by calcification in the tank, then the ions that remain are often described as having the same ratios of ions as natural seawater. Assuming that this is true, then the “residue” is simply more salt for the aquarium. Over long periods of time the salinity will build up due to this process (an effect that is quantified below), but there will be no significant buildup of specific ions in the tank.
In order to accomplish this, manufacturers could use a variety of calcium salts in the calcium portion, for example. They could use calcium chloride, calcium sulfate, calcium bromide, and a variety of other similar salts. They could also put magnesium and strontium in this portion as they would not be compatible with the alkalinity component.
The alkalinity portion of these systems is more complicated. As has been shown in other parts of this article, alkalinity can be provided as bicarbonate, carbonate, or hydroxide. I don’t know of any commercial supplements that use hydroxide for a two part system, but the commercial ones do use bicarbonate, carbonate, and mixtures thereof. Consequently the pH varies substantially between brands, and the various brands of these products should not be thought of as identical for this reason, if no other. In order to attain the natural seawater residue, the alkalinity portion could contain sodium bicarbonate or carbonate, potassium bicarbonate or carbonate, lithium bicarbonate or carbonate, etc.
I’ve not seen any independent test of whether these actually produce a residue equivalent to natural seawater, but I’ve seen no particular reason to doubt it, at least for the major ions. When it comes to the trace elements that might concern some reef keepers, it seems unlikely that these products will be any less prone to having uncontrolled levels of trace compounds like copper than are commercial salt mixes, or any other supplement of calcium and alkalinity, but that remains to be determined (at least as far as I know).
One issue that has confused some reef keepers, however, is the presence of trace elements. Assuming that these products are actually formulated with every ion such that a true natural seawater residue remained (let’s call this the “ideal” product), then it will necessarily contain such ions as copper. Since copper is elevated in some reef tanks, and is toxic to many invertebrates, reef keepers have wrongly criticized this method as adding more copper. That’s actually not what would happen. Since these products leave a natural seawater residue, and since copper may be elevated in concentration in many reef tanks relative to seawater, then using these “ideal” products will actually LOWER copper levels because when the increase in salinity is corrected, the copper will drop.
For example:
You have copper in your aquarium at 4 ppb and salinity of S=35.
You add a two part additive that over the course of a month raises salinity to S=36, and raises copper to 4.02 ppb.
Then you correct the salinity back to S=35 by diluting everything in the tank with fresh water, and you get a final copper concentration of 3.9 ppb.
Does this happen in real products and not “ideal” products? I have no idea. But the statement by manufacturers that it contains all ions in natural ratios, including copper, should not be viewed as a concern that it is exacerbating a heavy metal problem.
The rise in salinity of these products over time can be very roughly calculated, though there are several reasons why this calculation is only an estimate. For every 1000 meq of alkalinity added in this fashion (and the matching amount of calcium) these products will deliver on the order of 60 grams of other ions to the tank. In a tank with a low calcification demand (defined later to be 18.3 thousand meq of alkalinity per year in a 100 gallon tank (0.4 dKH/day)) this effect will raise the salinity by 3 ppt per year (compared to a normal salinity of S ~35). In a high demand tank (defined later to be 219 thousand meq of alkalinity per year in a 100 gallon tank (4.4 dKH/day)), the salinity will rise by 35 ppt in a year, or approximately doubling the salinity. Consequently, the salinity should be monitored closely in using these types of additives, especially in a tank with high calcification rates.
Many people have begun to use dosing pumps to deliver these sorts of additives more uniformly across a day/night period with less work by the aquarist. Such pumps can be obtained starting under $100 for each part dosed this way. There is no need to dose the magnesium part this way, since very little is actually required and once a week is plenty often enough.
The costs of these systems vary a bit. The original B-ionic from ESV costs about $34 for 1 gallon of both parts (10,600 meq of alkalinity), or about $3.20 per thousand meq of alkalinity. It has a pH raising effect, similar to my DIY Recipe 1. The B-ionic Bicarbonate version is more expensive, and is necessarily more dilute than is the original because sodium bicarbonate is much less soluble than is sodium carbonate. If your tank pH gets too high using one of them (such as the original B-ionic), then it is reasonable to switch to one that has a smaller pH raising effect (like the bicarbonate B-ionic or my DIY Recipe 2 using baking soda).
The DIY recipes can be far less expensive, depending on what grade of ingredients you use. Buying ingredients from a place such as Bulk Reef Supply will cost roughly $10 per gallon (total cost of all parts, so 1 gallon calcium, 1 gallon alkalinity, and a few cups of magnesium additive), or about $1.40 per thousand meq of alkalinity.