No one uses SAIII. Ever. Except as a joke, because beating someone with the worst super of the worst character in the game (and one of the worst supers of them all) is pretty awesome.
Pick between SAI and SAII based on the opponent’s character. Pick SAI when playing against most characters and SAII when playing against one that spends most of its time in the air or that dominates Q so badly that you need to get the most damage out of one opportunity you can get. Basically I pick SAII against Yun, Yang, Akuma, Ibuki, and sometimes Twelve, unless for example I’ve played against a certain Yang user before and I know he spends most of his time on the ground, in which case SAI comes out.
With the exception of generally unnecessary resets and a combo-vid-only combo or two, SAII has the same comboability as SAI does, it’s just that it deals more damage and can work as an anti-air. If you land SAI on an opponent who’s in the air, it’ll just hit a couple times, but if you land SAII you still deal full damage, and that’s great against the above characters who spend lots of time in the air or air-raiding you to death. Its higher damage output is great for playing against characters who lock Q down and barely give him a chance to breath; when that chance comes, you wanna hurt the opponent as much as possible.
There are some other notable properties of SAI as well. It can go through fireballs, for one thing, more or less negating Ryu’s denjin hadouken for example. It also has great reach. For example, you can punish even a max-range blocked shoto-sweep with it. It also does pretty good chip damage, just in case either you want to try to chip the opponent to death or something goes wrong and you miss like a standing forward to super. SAI is also better for random wake-up supers. Stupid and scrubby, for sure, but when Q is waking up he has precious few options. He can block, parry, option-select throw, or, uh… nothing good, basically. He has no good reversals that’ll stuff an impending throw or meaty. A super can do that. While both SAI and SAII have invincibility on startup, SAI can reach farther and if you miss, hey, you probably still have some meter or even a full bar left, and if the opponent blocks he gets chipped and if he jumps and you completely miss he’ll have to chase after you, and if he’s got someone without good mobility or he has no bar you’ll either be safe or just eat something simple. Again, wake up supers are a bad and way-too-risky strategy, but you’re playing Q, and you need every option you can get.