I'm sorry if it's been asked, but aside from appearance changes, what does the transformation do?

Very slight damage increase, speed increase, dodge increase, and some other useless changes. Super Saiyan is mostly for fun. It's the other two races who have a 'decent' transformation.

its just that with Super Saiyan you keep your skills so you dont feel as restricted as the other 2 but as ShiKage said its relatively useless

Its more useful with spirits as it doubles your total EP and helps VS mobs. In Pvp situations KoK is better for damage and crit

From a spiritualists point of view , increases attack speed by alot (ended up grinding just with normal attack , and the doubled EP can sustain my SSJ in combat quite a bit :D) increased move speed by quite alot , moving as fast as a person on that green bike mount wich is quite helpful for traveling + afew minor increases in energy attack , dodge , hit rate.
So if u were trying to figure out if its worth getting or no id say if ur a spiritualist id say SSJ should be a priority for ya , if ur a MA id say just stick to kaioken since it has similar bonuses like SSJ (the atk/move speed bonus , slight increase in offensive stats) + kaioken can increase ur crit/energy crit rate further if u use it multiple times.

SSJ is just a buff that increase some of your stats and makes ya blond.

They need to add super saiyan 2 and 3, I mean kaioken gets quite a few X's, if they did I would be back to the hell of collecting dragon balls haha. I like SSJ, I died twice on this one boss with 2 mob helpers, went SSJ and took him down so I feel it helps quite a bit!