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#4 It supports wireless inductive charging without a bulky sled
Ever since the ill-fated Palm Pre's Touchstone inductive charger, I've wanted wireless charging for my phone. There are add-ons for the iPhone that provide that capability, but they're large sleds that strap around the iPhone and make it bulkier and uglier than necessary.
Because the Galaxy S4 supports replacing the plastic back, you can simply pop off the stock back that comes with the phone and snap on the new back and you have a phone that supports wireless charging, straight from the manufacturer.
There are a few disadvantages I've discovered. Otterboxes won't fit, because they're built with absolutely no tolerance for "gooshiness" around the frame, and the S4's wireless charger adds about a 1/32 of an inch extra bulk to the back of the unit. Also, if you want a wallet-style case (most of which merge their own back into the phone), you're probably out of luck.
Even so, the few case disadvantages are worth it for integrated wireless charging. My new Android phone has it and the iPhone doesn't. I've always found the lack of iPhone wireless charging rather strange. Wireless charging seems like such an Apple-like thing to do, it's somewhat odd that the company seems to have thusfar ignored this incredibly convenient technology.
Image courtesy Samsung.