Yep if you use tc you can actually see the difference. When I used ni200 30g I only needed around 10-15 watts in my kf5 at 410-420f. With 26g SS304 I need around 20-25, during the preheat it's around 40-55 watts for about one second. Thicker wire needs more power. I've got a clapton build, in my velocity, that needs 150 watts to get a nice warm vape.
I feel like TC (and I mean really diving into TC) is the best gateway to a more practical understanding of the balancing act that is coil building, for regulated users. You don't see seasoned mech- or TC-users baffled by this interplay very often -- and that's not some indication of intelligence or superiority or anything of the sort! But I feel like those styles of vaping really force a user to have a more comprehensive understanding of the whole works, and eventually this becomes somewhat innate.