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Well it depends on what you want and going to use it. If you are plaining to use it to watch movies/ youtube search the web i say you go with the GS3. If your going to use it just for calling, texting, surve the web a bit then go with the GS4 Mini. Also have you thought about the Samsung Galaxy S4, thats a pretty good phone too and its new.
Well the big decision is do you want to pay the Smartphone Lite price or the price for a full Smartphone. Because if it is the Lite price go for the S3 Mini. If the full Smartphone go for something like the real GS4/One/G2 as the only difference is the upfront cost which you can get for sale at like a Best Buy or Future Shop