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It all depends on what you use your phone for Mabet. If you're wanting it mostly for entertainment reasons, Movies, Games and the like the S4 with the almost 5 inch full HD screen is probably what you want. Not that the S3 isn't a strong gamer and entertainer mind you, it's just that with a 5 inch screen you have more real estate for things like control buttons and subtitles.
I own both, and ill give a few things I like about the s4 that i didnt realize before i bought it. The phone physically feels much tighter. But volume buttons, power button, and home button are much more flush with the phone and feel better when pressing them. the battery door also fits better, so mainly build quality seems to have gone up, but i thought the s3 was fine, and i still think it is, but it is hard to go back after getting used to the s4. It is also more rectangular so it feels better holding it. The screen is also a big improvement, much brighter and easier to see in daylight. really the big things are physical improvements to the phone, there are new software "gimmicks" that are actually pretty neat and less gimmicky then they may seem, but i wouldnt pick the s4 over the s3 for these features. So really, if you like the feel of the s3 and want to save some money, go for it, its a great phone and i would recommend it to just about anyone. if i were to recommend the s4 to someone, it would be because of the physical feel of it, and the screen, which really is quite an improvement.