Sol's privilege vs the rest of the cast comes down to the completeness of his toolset coupled with his huge damage. He is a straight forward character to use with multiple ways to get in against the opponent, has the ability to pressure the opponent in neutral with relative ease, and also strong okizeme*. He's basically the complete package with only the most minor deficiencies you would expect to find in a fighting game character. For example, Ky has incredible neutral and oki tools, but relatively low mid-screen damage to compensate. I would say Sol's most significant weaknesses is his relative predictability in approaching the opponent.
Sol is good at all the above because of the following tools:
His 3 frame 5K - the fastest normal in the game, tied with Chipp's 5P. It can be used to find gaps in opponents' pressure with far greater ease compared to other characters. It also leads to full combos that deal huge damage from such a fast starting button. This button also works as an anti-air against many opponents' moves. This is significant as it's faster than 6P (the dedicated anti-air button for every character) and leads to much more damaging combos (though the Sol has to commit to these whether or not the 5K connects, making it a bit read-dependant). Still, it's crazy Sol can use this button on reaction, rather than having to spend more mental effort predicting jump-ins like other characters, and gets more reward for doing so. The only downside of this button is that it has long recovery on whiff.
Far slash (aka fS) - this button is +2 on block, and has deceptively long range. You will see a lot of Sols bullying opponents by just spamming fS over and over until they get a hit. Although fS into fS CAN be interrupted, the opponent has to be brave in order to do so, as Sol has two options that will beat this - either a delayed gatling into 5H or a frame trap using 5K or 2K, both of which lead to a big combo. Also, the expectation of Sol pressuring using frame traps and strike pressure means he can often use this button to scare the opponent into sitting still, in which case he can run in and throw, leading to a knockdown and oki. Throws are extremely safe in this game as there's a very easy Roman Cancel option select you can perform as long as you have 50 meter to cancel the whiff animation, negating almost 100% of the risk.
6S - An excellent mid-range button that has stellar active frames, making it great as a neutral footsies tool, punishing backdashes and pressuring opponents on their wake-up. It's also a great combo starter, especially on counter hit which makes combos very easy to hit confirm into. Although 6S can be punished as it's negative on block, Sol can cancel it into a special to make it (technically) safe; everything that it cancels into is generally punishable. But, by delaying the cancel from 6S to the special, Sol can catch the opponent out, meaning that Sol rarely gets punished for just throwing this move out.
Clean hit Volcanic Viper - This requires some setup/skill to execute, but under the correct circumstances, Sol's H volcanic viper can deal extra damage to the opponent and earn him a hard knockdown, leading to an extremely strong oki situation for Sol. It's kind of crazy that clean hit VV does both these things - one would be enough, but both is pretty absurd; see this clip of me fighting a Millia recently:
As Benny says, he's top tier for the moment, but not nearly as bad relative to the rest of the cast compared even to other GG titles. Johnny and Elphelt were many, many times more obnoxious even in the Xrd games - Johnny could skip neutral for 25 meter and set up genuine unblockables which led to stupidly high damage, and Elphelt could combo into knockdown from almost any hit, forcing a weighted game of RPS every time, as well as being able to do absurd frame trap pressure with her shotgun and grenade nonsense. And going back to XX, Testament, Zappa and to a slightly lesser extent Eddie were all so obnoxious at filling the screen up with crap and locking the opponent down that the game basically became 1 player...
Anyway, it'll be interesting to see how Sol ends up in the long run as a fairly simple but powerful character. He's obviously strong at the minute, but these types of characters only tend to do well for so long in fighting games. I have a feeling characters with more potential for grimy setplay like Chipp and Ram will become more dominant in the long term. Not that we're really seeing many Sols actually win tournaments; though they're always placing very highly.
*Also known as "oki" - this is the art of pressuring you opponent as they rise from a move that has knocked them down.