If your PC isn't from ancient times (I play on a laptop from 2010 which was mediocre even then), performance on it should be perfect ("perfect" here meaning you may crash sometimes as the game starts or w/e, but every hickup is entirely inconsequential).
PS4 has some hassles atm since it's a fresh launch, but those should largely be fixed soon. No real issues with either by next week, I'd presume.
PS4 has the "2nd Encore" features such as voiced Storymode and Trials - those aren't on PC yet and we aren't 100% sure whether they ever will be, so if you care about those, PS4 is the way to go. PS4 also provides crossbuy with the Vita (you buy it on PS4 - you own it on Vita as well), so if you want to play on your handheld sometimes, that would definitely be the choice to go for.
PC has Lobbies (a way to play with 2-7 other people "at the same time") which aren't yet on PS4, so if you want this as a feature on launch, you'd have to go with PC for now (will arrive on PS4, but again we aren't sure when exactly)
PC has less input lag than PS3; I don't own the PS4 version so can't comment there. Doesn't matter too much though, you get used to it quickly enough when playing and it's barely even a bother if you keep switching between the two versions.
PS3 is the current tournament standard (maybe PS4 in the future).
Community is much larger on PC and periodically explodes for some periods of time due to Steam Sales and Free Weeks etc.
PS4 may close the gap a bit (especially since there is crossplay to PS3), but I'd still presume that most players -and especially most good players- are to be found on PC.
Netcode is the same, but I think the PS3's implementation is a bit shoddier and/or people are more likely to play on it wireless/with a shit connection. Everything feels notably laggier while playing online (+ of course the higher input lag making things worse). Again, not sure how the PS4 version clocks in here.
Note that with "shoddier" and "worse than PC" it is still the best netcode in the business! It's not bad or anything - the PC version is just the by far strongest netcode out of every fighting game there is, and the PS3 version falls slightly short behind that while still being topnotch.
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What I'd do would be to buy the PS4 version, which has a bunch of cool features right now (aforementioned 2nd Encore extras) that make the game more engaging, while the PC specific feature (Lobbies) won't be too much of a thing for beginning players in any case.
Then after playing on PS4 for say half a year (which will be perfectly fine - the community IS smaller than on PC, but you still find matches readily as long as you aren't from some no-man's land), you can check out the Steam Store during the next big Sale, and buy SG there as well when it's 75% off or whatever.