What exactly is the difference between 4.10 and 3.73 gears in a 2003 gt?
 

Which is better and why?

Don't fear the gear. I went from stock 3.55's in my '06 GT to 4.10's....one of the best mods I ever made. First gear was pretty shallow, but cruising at highway speed in fifth gear wasn't much different from stock IMO.

I have had 3.31, 3.55, 3.73, and 4.10 gears in mine. I like the 4.10s the most. With that said, I currently have a 2.95 1st gear in the transmission. If your 1st gear is lower than that (say...3.35:1), the 3.73s might be a better choice. When I had a lower 1st gear, the 4.10s were a bit of a pain. I would roll 10 feet from a stoplight, and have to grab 2nd. In fact, 1st gear was pretty much redundant.

I have 3:73's in my 08 Bullit. It's just about right. The issue with 4:10's or any other gear set, is that if not installed by an expert they can be very noisy or wear badly.
The higher the ratio, the more noisy they tend to be. Besides, I'm at the highway speed limit at the end of second gear. These days big speed can get your car impounded and your licence gone. There's not many places you can let these babies "eat" except at the track. So if you want 4:10's go for it!. Probably only a couple hundred RPM extra over 3:73's.. Enjoy.