I have an S3 and an iphone 4 (not 4S), the S3 lags with the new OS and multiple apps open. I'm always using my iphone for calls and messages, but browsing the S3 screen can't be beat for the size.
My friend has the HTC one with the speakers in the front and that is an amazing phone although battery life is pitiful with it (same with my S3). It also has the remote control feature due to having infrared.
If you want a good purpose phone with excellent battery life, I would suggest an Apple phone (the 4S should be practically free now) and mine lasts about a day (used to be 1.5 days, but it's 3 years old now).
I don't see an advantage to having an S4 other than some extra features that you'd probably never use. If you want a Samsung, the S3 will be fine. Great phone just lousy battery life.