Around the next iPhone introduction Sony will be bringing their new phones to the market, including new models with LTE, Snapdragon S4's and a killer camera. It'll be the phone that mr. Bond will use in his next movie ^^
I actually really like the Xperia S as it is, but if they're going to be doing better I'm all for seeing it.
As for the original question, I'm inclined to say wait. You haven't said you need an upgrade for your SII urgently, so you could stick with it for a while longer. With the large development community still around it you probably could have a good bit of fun with the phone, even if it is no longer the most powerful. If nothing else, waiting means you'll be able to survey the market before you buy anything. If you want an iOS device you can definitely go down that route but it's worth waiting for Apple's latest and greatest.
Even if you decided you didn't like it after taking it as your upgrade you could sell it on eBay within the first month or so for an inflated price, as people will clamor for them. From that you could buy an Android device of your choice. By the time the next iPhone is out you might have your heart set on one of the Android phones on the market. I've used an SIII but only for a short period of time. The body doesn't feel as cheap and nasty as I expected. It definitely feels plastic-y, but not horrid. I imagine it would be okay really. I haven't been able to get any time with a One X unfortunately, so my opinions on it are nonexistent. I like the sound of the polycarbonate body, but that's not much to go on.
Waiting does seem like the best option. Specs-wise, the SIII is better in some regards and the One X is better in others. The SIII is faster, but in real-world terms both phones are that fast that the differences would be fairly minor. The One X has the better screen and probably a better feeling body, but as someone said above the battery life is meant to be pretty terrible. I suppose it depends on which phone you like the look of better. They're quite equally matched I guess, so choosing one over the other would be a challenge without having held both of them and simply chosen on the spur of the moment. I suppose since you've flashed ROMs to your phone and stuff you might like the one with the bigger development community. I haven't checked which one that is but my guess would be that the SIII has the bigger community. It's just a guess however, based on the SII's development community. From what I've heard the SIII's screen is a challenge to see in bright daylight, but when I used one I was in Northern Ireland, which is dull 364 days of the year, and I could see it just fine.
The competition in the phone market is a great thing, since each flagship device is really nicely polished. Apple's iPhone, HTC's One X and the Galaxy SIII all have their specific merits. I'd wait and see if anyone can change it up a little more. The sII is still a good phone, so good luck with your decision.