Which rpg has the most unique and workable approach to superpowers?
What do you mean by "unique"?
I mean I find the Shard powers that are essentially magical mutations in Providence really neat--the idea of where they come from and how setting wise is interesting. Rules wise however they're kinda bland "buy level, get X amount of stuff."
Hearts & Souls doesn't have a huge number of superpowers--because anything you can describe in plain English can work as a power--you just describe it, give it a rank/scale structure and go to town. Mind you there are numerous examples in the books for how things work (Regeneration, Body Armor, etc.) because the system is very broad strokes and abstract.
Powers can be done as above, or broken down into "Attack", "Defense", "Manipulation" and "Movement" to indicate where they might be best at one thing, and poor at another (or unable to perform stunts that fit that category..at all.)
Is that unique? I don't know. It works though.
M&M, Hero, Living Legends, Godsend Agenda/D6 Powers--all have "purchase X points to purchase ability and get Y effect(s).".
Truth & Justice is pick power give it a rank (from a choice of rank combinations from High Rank 1 power, to low ranks many powers)--it can be a metapower (very flexible), or a power in general, and has a penumbra of effect it is capable of covering.
Sketch is pretty interesting, as you get powers assigned but why you sketched/drew/cobbled together as an image, and has a stat called "Power" IIRC that determines how well you're power works.
Marvel Superheroes (OOP) used a similar system to H&S--get a power give it a rank of effect (although randomly rolled is one default) and that is how strong/effective the power was. Many powers could be made up using plain English and the rank.
Wild Talents uses Attacks, Defends, Useful Outside of Combat, and Robust or something like that which determines how much it costs in points to buy an ability and how much effect it has for that cost. (Something that only Attacks does more damage for the cost than something with Attacks and Defends) it is a bit complex because of the "if/then" nature of balancing how broad the power is versus how strong it is.
I like the V&V random system. It creates unique combos that you would otherwise never think of. Some of them are total stillbirths, of course, but usually you get something workable, and occasionally you get a total gem. Furthermore, V&V is the only game that I've played that effectively models the wide range in power level that comics exhibit. You can roll up superman or Robin, or Paste Pot Pete for that matter.
The game is definitely old school clunky though, but fun to play non the less.