How similar? Relative levels of all of them are potentially big factors in comparing the two tanks.
Zero phosphates at 10,000 lux would be a lot better tolerated than at 20,000 lux....and those levels don't always look all that different to the naked eye.
Are you using the same light fixtures at the same mounting height with similar programming on both, for example? Or do you have a light meter to compare them?
Flow is pretty hard to characterize since it's more or less invisible.

But are you at least using the same pumps and a similar rock layout in both tanks?
Also, 5 ppm NO3 (listed for your melting tank) might actually be pretty high to throw off equilibrium under the circumstances. PO4 is very crucial.
The tank with 0/0 ppm isn't ideal, but at least it's balanced where it is.
You might find some more good, related links in the
Nutrients section on my blog, such as:
Results of the 1991 United States-Israel Workshop, “Nutrient Limitations in the Symbiotic Association between Zooxanthellae and Reef-building Corals”
Heck of a title, but dig this one quote and then go click and read it....especially the bolded part and what follows....it's your melting tank:
"…the argument is made that under normal conditions in nutrient-poor tropical seas, zooxanthellate corals are successful because they are closed systems with respect to nitrogen. Growth of zooxanthellae under these conditions is not balanced with respect to fixed carbon because of the low rate of nitrogen supply.
As a result, the excess carbon is translocated to the animal host. Increasing the nitrogen supply leads to rapid growth of the zooxanthellae, with consequent reduction of translocated carbon to the host. Eutrophic conditions allow the zooxanthellae to outgrow their hosts and the host loses control over the population of its symbiotic algae. Thus, maintenance of a balanced coral symbiotic association appears to require low ambient nutrient concentrations."
There's another great article linked at the bottom of that one you should also read.
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