Neither your first or second point would be the reason. If you really had an S3, you would know the screen shuts off within a second of the phone going to your ear and turns back on when you pull it away. Experience would tell me that you had more info pushing to your S3 than the iphone, or you were running another task in the background (you know, real multitasking), or you were running the int'l version S3 that had the drain value improperly set to 34mA, instead of 3.4mA. Easily fixed. The 4s battery life is a joke in comparison to the S3. I give you Apple's own words from 10 months ago:
The 4S works the same way, the screen shuts off when I put it to my ear. But I never use either phone that way. I use a BT Plantronics Voyager with both.
As for multitasking...possible. I don't take the time to shut down apps on either device. I didn't realize that the S3 keeps burning power for apps not in current focus, however. But even then, I'm only running web browser, email and maps.
Shrug....don't know what to tell you. My experience is that I get far less power out of my S3 than I do equivalent use out of the 4S, and I'm essentially using them the same way, just on alternating days. Well that's not true any more....I've gone back to my 4S for most of my weekday use since I need the battery power for business calls. I do still use the S3 on weekends, however.
If I've the time, I'll set up a side by side test where I set both phones up to call each other starting on a full charge, no apps running other than email and browser, and just let them burn down. I'll even run a stereo by the phone on either side to simulate speech, enable two Voyager BT headsets and let them burn down the battery in a race to dead. Then, guess I'll know for sure.