I have had my HTC One X for a little while now, so this is what it is like to own one, and compared to what I hear about the SGS3 as well.

• Screen - Pure and simple, the best phone screen of all time so far. Ridiculous resolution, vivid colours, bright, doesn't wash out too much in the sun. Superlative in every way really.
• Size - Well, its big sure. 4.7" screen, but I wouldn't say it was too big, I really think that it offers a significantly better portrait typing experience than a 3.5" phone. I swapped out my Nexus One for a Desire Z really fast because I simply couldn't get on well enough with the keyboard - but this thing, I can type fast and error free straight out of the box. It really is better than having real buttons, and I am normally a real buttons guy. The biggest issue with the size is that it is a stretch to reach the power button with my index finger, you do have to alter your grip on the phone to do this one handed, and lose the support of the bottom of the phone with your pinky or thumb. I don't know if I have explained myself well there. It does fit into my pocket just perfectly fine, helped by the fact it is fantastically thin and light. I honestly think it is the perfect size, its not exactly a Galaxy Note but it is still just as much of a joy to use. I like it.
• Physical design - The curves on the glass, very discreet LED notification, nice button action, its all great. Way nicer than most Samsung phones that I have played with. Not having a removable battery or SD card hasn't worried me much when I considered how many times I actually removed the battery or memory card in my old phones (zero). Undocumented suck feature though is that since you cannot pull the battery there is a reboot function on the power button which reboots the phone if you hold it down for about 7 seconds. Sit down for about 7 seconds and often the phone reboots in your pocket. By far the most annoying feature of the phone so far.
• Phone features - The camera is really great, it starts up practically instantly and has zero lag as far as I can tell (http://hussein.jodiyawalla.co.uk/temp/IMAG0070.jpg is a sample). Image quality at 100% crop is very phone-like though, but I think is just about good enough to replace a point and shoot. It doesn't seem like the LED flash works particularly well, the colours come out wrong and it feels as though it needs a diffuser over it as it gives a bit of a spot beam. The video quality is great (http://youtu.be/WZeEWr9Twug?hd=1 is a sample). In call sound quality is very good too especially to the other party with its dual microphones, the speaker phone is clear and it seems to have a speaker on it which doesn't distort much which is surprising for a HTC.
• Performance, Software - It is plenty fast. To the point where it doesn't seem like you are waiting on the phone to actually do anything. There are no eggtimer/beachball please wait moments. Apps open in a blink of an eye, there is no lag, the phone does things as fast as you can move your fingers. A cold (fast) boot is around 10 seconds. I don't wish it was faster. Along with most of you, I wish it didn't have Sense and was a more stock Android phone, like a Nexus. I've already rooted mine and installed a MoDaCo custom rom with a bunch of the Sense things removed and replaced with regular ICS versions. I'm extremely happy with my efforts and I would say that my own hybrid hacked up software is pretty great. Honestly though, out of the box the HTC software is really not that bad. It doesn't feel like it slows the phone down and a bunch of applications can be disabled so you can effectively debloat your own phone without risking your warranty.
• Battery - I use my phone for some emails, talking for a few minutes, some gtalk and sms messaging, bluetooth connection to the car, wifi and gps always on. It does last all day. I'm reluctant to use the phrase 'easily lasts all day', I seem to be getting 10% battery left at bedtime. This is not exactly reassuring, especially since the phone is new. It doesn't have a better battery life than my old Desire Z, but I think maybe I do play with it more. Android says the screen uses 47% of the battery power.
• Compared to the Galaxy S3 - The S3 is likely to be better. The camera appears to be a little better (although the camera software on the HTC is better), sure it is a little bit faster too. People may go on about removable batteries and SD cards, but so far its all small differences to me. The big upgrades are that it reports to have significantly better battery life, and the power button is on the side rather than the top. When I bought my One X, the S3 was working out to be around an extra £150 over the length of the contract, and so I'm pretty happy with my choice.