I had both keyboards (and still have my T4). I'll try to remember as much as I can.
The T3 was my first introduction and experience of the Tyros range after taking a bit of a break from Yamaha, before that the last Yamaha I had was the PSR 8000.
It's a good question you ask because there were some differences, some where bigger than others.
I think one of the biggest ones for me was perhaps the time it took loading from start-up if it contained user or UVN data from boot, if you had extra sounds or styles or even expansion packs, the T3 would take an age to boot, I think nearly 3 to 5 minutes if you maxed the memory out. Whereas when I got the T4, with the exact same set up, it takes about 30-40 seconds to load all of it! I was shocked with that alone.
I think the T3 only uses the .wav format and not .mp3 so you'd have to convert the file first which can be a bit of a pain.
I think the T3 has 80gb hard drive, were the T4 has 250gb. Not a real biggie but still a difference.
Another difference I noticed was the overall sound between the two. The T4 seemed have a warmer sound than the T3 since it had more DSP's.
The T4 introduced some new drum kits that made some styles more live sounding such as the Studio Rock type stuff as well as the Swing & Jazz sections with the new Brush kits.
But in terms of sounds, the biggest difference of all was the addition of vocal voices although at the time I remember not many peeps here were that bothered about it, some said it was a little OTT especially as a lot of them were used in styles, but I find them make a difference as long as they are not in your face and are used just to fill in the background such as how some of them are used in the Latin styles.
Key feel was the same that I can remember, the actual keyboard design itself is exactly the same apart from the green lights in T3 and blue lights in T4. In fact, I think the T4 has a better build quality because I remember posting a thread here voicing my concern at how easily the silver paint was rubbing off from some of the buttons whereas on the T4 I've had no such problem and I would have had the T4 longer now.
More SA voices but I don't think there were that many more. The screen display / resolution was the same although there is slightly more colour in terms of the icons it uses on the T4.
I can't think of anything else really. I really enjoyed the T3 but when I got the T4 I thought it was better in almost every area, some bigger than others.
Oh, and you also have that option of the T4 10th Anniversary Edition model in black which looks gorgeous.
Depending on the price difference you can find the T3 over the T4, if you're not that bothered about any of the improvements and additions of the T4 then the T3 is still a great keyboard.
I hope any of that helped.
Ketron SD7, Pa1000, Tyros4, SX900