If you plan on going Android, go for the Nexus 5 which should be out by next month. I've never understood why someone would want the bloated software that is Touchwiz. Full of gimmicky software which really has no use. Why in the world would you hover your hand above the screen when looking at pictures and such? Swiping with a finger is much faster and easier. That's just one example. All those "features" just slow it down.
To the poster saying the S4 has a better camera than the iPhone 5S, lets wait for reviews before jumping the gun. Of note though, the iPhone is always known to have a top camera, and this past generation I'd say the only phone that had a camera better than the iPhone 5 was the lumia 1020(I believe that's the one). Samsung galaxy S3 wasn't even in the same ballpark when it came to low light pictures. There are plenty of review sites that back it up.
Care about battery life? iPhone no question. iPhone 5S is rated for 10 hours of use.
Worried about the fingerprint sensor? I don't know why you would be though, Apple will never have your fingerprint...they will not store it in their servers or whatever. Either way, if you're worried, just don't use it. Simple as that.
iOS is a lot easier to use as well. If you're deciding between the S4 and 5S, I say iPhone no question. If you want an HTC One Nexus edition or say a Nexus 5...then that's a harder decision as stock Android is very good. I say iOS all day everyday, but you can't go wrong with stock Android either.
If you game a lot on your phone, I'd pick the iPhone 5S.