Just my 2pence, I think the ultimate weapons should keep their special damage formulas 
it makes them more interesting to use, I like how cloud's ultimate weapon has an opacity visual as to the damage it will do, and Yuffie's can use morph at full attack power. Things like this make experimenting with them more fun.
To be fair, the ACTUALLY interesting ones are few - and half of them are Yuffie's Conformer, both because of the lvl-scaling and because of the Morph quirk.
For most of the others, the formulas aren't great. HP/MP based ones are boring, and feels-bad moments when you happen to get hit/drained. Missing Score is tough to get right between totally OP and sub-par, but also feels like a somewhat bland hoop to jump through for what's nothing but a static modifier that barely if ever affects how you play. Limit-Bar-based is interesting, but I personally also never liked it because it's either discouraging you to use limits or makes you feel like a wet rag during downtime when you do use limits.
I guess the question is: what role are ultimate weapons supposed to play? Are they supposed to be the #1 no-questions-asked go-to pick at endgame? Are they supposed to be extremely good in extremely specific circumstances, and not that great outside of them? Or somewhere in between?
Ironically, the gameplay that probably feels most like an actual ultimate weapon is the status shenanigans with Tifa - charging a weapon's power by balancing negative statuses feels like an actually meaningful gameplay decision (even though Curse Ring, and to some degree Death Force/Added Effect stuff, kind of makes Death Sentence way too easy to deal with). I'm not sure how much can be done given engine/combat system limitations; FF7 isn't the most complex in that respect.
Possible ideas that come to mind (with no regard as to how feasible they are to implement): dealing magic damage (vs. MDEF not DEF); auto-debuffs (e.g. Berserk, Dual, etc.); buff immunity; negative status buffs (e.g. -255 DEX etc.); zero materia slots; zombified.
I like that in some cases earlier weapons can remain competitive; I don't like that most of those involve DEF-ignoring weapons that make certain fights a joke (e.g. Ruby Weapon). Of course a mid-game weapon shouldn't be an endgame contender all the way through except in very rare circumstances; certainly they shouldn't just eclipse every weapon between when you get them and endgame (hi there, Powersoul). The lower AP burden in ANT has done a good job weakening the power of double/triple growth weapons, which is good; but there's also too many too good triple growth weapons still (hi there, Powersoul. What, again? geez.) which makes differentiation more difficult.
Overall, though, NT has a lot more variety in weapon choices - and, above all, MEANINGFUL choices - than the original which is fantastic.
