I think you have recieved plenty of answers to your questions so I will just offer my opinion after playing with a coworkers GS3 over this past week. Keep in mind that I was a G2 owner. The G2 died and I needed a phone. All 3 of my lines were due for an upgrade and I had every intention of buying the GS3 but it was not released yet so I bought the One S and was going to give it to my wife once the GS3 came out. Things have changed.
The GS3 seems to be right on par with the One S as far as speed and usability. They are both blazing fast. He tried to impress me with the floating video feature but he was amazed when I showed him the same thing but with 2 different videos running while I flipped through flipboard. In fairness, that feature is much more accessible on the GS3 than on the ONE S.
The size of the GS3 is a put off for me. I was surprised at how comfortable it was in my hand but still too big.
The glossy finish on the GS3 would drive me nuts. The guy who owns it complained that he had to carry a cloth to wipe it down because the glossy finish showed every finger that ever touched it. It also had this sticky feeling like a 4 year old had just been playing with it after eating PB&J. It was kind of a nasty feeling. I have a 4 and 6 year old and deal with that enough already.
Build quality didn't seem to bad but after the bulletproof G1 and G2, I really don't want that plastic feel with my phone. I also don't find it as attractive as I thought I would. He obviously has the blue version and it is hideous to me. The white may look better but looks too much like an Iphone to me.
The GS3 does have a lot of cool little features like swiping your hand across the screen to take a screenshot or tilting to zoom or touching the lockscreen and then flicking the phone to unlock. The problem is that I watched him try to make it work a couple times with each feature before it actually worked. It may be better once you get the hang of it but I am sure I would use them for a week and then turn them off. Gimmicks in my opinion.
The One S also has its issues.
The multitasking isn't very good. I do love it though. The multitasking button is my most used button on my phone. It may reload but it doesn't bother me as much as others.
There is no grip with the phone. Angle it too much in hand and it will slide right out. This does not happen on the GS3. As stated earlier, that thing is covered in PB&J and will stick to your fingers in a near vertical position. You can even shake your hand around and it will stay put.
Having a removable battery isn't an issue for me. I have a charger in my office at work, a good car charger, one next to my bed, one in my kitchen and one in my home office. I can't really comment on the battery life as mine is rarely below 70% due to the fact that if I am not using it, I just put it on the charger. I am at work right now and it is fully charged but I just leave it on the charger since I am not using it.
Not having expandable memory is a bit of an issue but not much. I have a bunch of dropbox space and an FTP setup at home. I have been moving stuff around for sometime now. Probably wouldn't change even if it did have expandable memory.
All in all, I have decided that my wife can get the phone of her choice. I will be keeping the One S for myself. She wants one also though as she has fallen in love with mine. The GS3 is a great phone but not for me. That is my opinion though.
Good luck to you. You will probably be satisfied with either phone. Just don't buy into the One S is crap and GS3 was made by GOD fodder. They are both great phones that will appeal to different folks. That doesn't make either one bad. Just different. It is all about what makes you happy.