The second is a bit more complicated, with each power having its own little rule or condition attached to it. These are your Moves in Fellowship, Charms or even Merits in Exalted, or Foci in Stars Without Number. Those are the meat of things usually - something flavourful and interesting.
However, sometimes those powers are very bland, amounting to nothing more than a to-roll bonus under certain circumstances, essentially turning into conditional stat bonuses. It's important to keep this difference in mind when designing an RPG.
To illustrate this point a bit more, let's talk about some examples.
City of Mist - heavy on the stats
Our first kind of powers are essentially stat boosters - something that modifies some specific roll for your character. They can give flat bonuses to rolls, change the odds of a roll, give some conditional re-roll, or something to that effect.
Stars Without Number's Specialist Focus,
a good example of a bland power.
One of the more prominent examples of a game that is heavy on the stat powers that I've come across is City of Mist. It's a Powered by the Apocalypse game about being a super-powered person in a mysterious city. You build your character by choosing their themes (Mythos - magical powers, and Logos - mundane experiences) and picking power tags from those themes. For example, if you had a Divination Mythos, you could pick "Sense minute earth tremors" and "can hear a pin drop".
Power Tag questions and answers
Now, knowing that this is essentially a Powered by the Apocalypse game about being superheroes, one would expect the characters to have some cool, unique powers to play with. But no, most of the system is just the core moves everyone has access to. If you want to attack someone, you "Hit With All You've Got", roll your dice, and then add +1 for every tag that's appropriate. So if you have "fast as lightning", "predict a foe's next move", "see in complete darkness" and they apply to the situation, you roll with a +3.
The powers you have don't change what you can do, only reflavour how you do it. Someone with an Adaptation Mythos could throw lightnings, one with Mobility Mythos would strike fast, while one with Training Logos would punch them like a boxer, but the roll and the rules are the same in either case. Almost every power you get in the game is just a conditional +1 stat.
There are some other mechanics at play in the game of course, how if you specialise in one Move you can roll well and have some more interesting Dynamite effects, how your powers define who you are and if you neglect some aspects of yourself you get a replacement Mythos / Logos, etc. The core of the game, however, relies on powers that give you just stats.
Chronicles of Darkness - when quantity turns to quality
One asterisk that one could perhaps add to stat-heavy powers is that sometimes given a large enough shift in the stat, the game could feel vastly different. For example, in our Creepy Rashomon Marine Buffet game of Vampire the Requiem, my character had a Dynasty Membership Merit that let them become Tasked and give them an 8-again quality on rolls (basically - you could snowball your successes a lot easier, meaning you were more likely to get exceptional successes). This combined with some high dice pools meant that for a very specific goal my character turned into a hyper-focused, hyper-efficient machine akin to T-1000...
Nothing can stop a Tasked vampire! Exceptional success!
So eventually, given a power that shifts the probabilities of your rolls a lot, or otherwise helps your rolls a lot, even a bland stat boost power can feel amazing for a time.
Magic - mostly powers, few stats
While I couldn't think of a system that relies mostly on unique powers without much in the way of stats, one aspect of games that usually falls in this category is the magic system. Even in D&D a good number of spells each come with their own rules and special systems unique to that spell, and spells themselves take up about 1/3rd of the Player's Handbook.
Even a simple Alarm spell adds something unique to the game
Stats vs powers
So, on one hand of the spectrum we have bonuses to stats (numerical increases or other special but simple modifiers, rerolls, etc.), and on the other we have powers that each come with their unique rules attached. One is not better than the other, however.
Stat powers are easy to add and test. You can predict what changing a stat by +1 would do to a roll.
Powers that come with their own mechanic have to not only be tested by themselves, but also against and in combination with other mechanics and powers. Each is a special use case and an exception, possibly bloating the game (how many "harm someone" or "heal someone" spells do you really need?). Adding more and more special rules can also be a burden when you have to remember to use them, unless they are well segregated into their niches (you don't need to think about special hacking rules during a shootout, and your battle spells aren't needed during a conversation).
Ideally, you'd want a complimentary mix of both in your system - powers that rely on stats to perform better and better, and stats that are varied enough to cover the basic rules without having to resort to powers for everything. Chronicles of Darkness lines are a pretty good example of this.
