Both methods work for ich, but if you think this is velvet, should do copper. TTM is really only for ich, unless you reduce the tank transfer time to 36 hours instead of 3 days (per humblefish).
In regards to TTM vs copper for ich. I have done TTM a lot in the past, and have just done copper treatment recently. My opinions having down both: TTM is more labor intensive, but for the less experienced, it's easier not to mess up and kill fish. Copper is easier in terms of labor, but you have to test frequently, and watch your ammonia levels. There will be differing opinions, but I almost never lost a fish doing TTM, and going through copper at therapeutic levels recently I lost a couple fish.
In terms of equipment, TTM needs more equipment (you need two sets of tanks , heaters and airpumps), but to copper you need to get test kits and reagents (would highly recommend the Hanna). TTM requires more water, obviously.
Hope this helps.