sora :
I'm looking for either an iPhone 5S or Galaxy S4. Can someone recommend me which one is the better phone? Also, is it safe to buy one of these phones off of Amazon?
Like Pinhedd said, it's about preference. If you have invested lots of money in the Apple ecosystem, go with the 5S, and vice versa with Android and the S4. You have to take form factor and usability into account as well as some less 'techy' people do struggle with the Android OS.
Your best bet is to go and try the phones out in store, and see which suits you best.
And in response to the Amazon part, yes it is safe if you buy direct from Amazon and not from a 3rd party seller.
Hope this helps

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