Roomie just upgraded to a Droid Maxx the same day I got my 5S. The Battery Life isn't even in the same Stratosphere, the Maxx easily gets 2.5-3x the battery life of the iPhone with same type of usage.
I took the iPhone back and exchanged for a Galaxy Note 3.
I think the small screen was decent for one handed usage and portability, but for working with Media (which is what I do a ton of, using mobiles for sports video analysis, etc.) leaves it as a pretty inviable alternative compared to bigger Android devices - and Windows Phone doesn't have the apps I need so the Lumia Icon wasn't a viable candidate for me to buy.
I also think Apple skimped a bit too much on Specs, and don't want to be left with a device which has degraded in performance noticeably in 18 months or so. I paid cash for the phone and $749 + Tax is simply not the kind of money you plop down with doubts.
That being said, the Note is probably the phone I should have gotten to begin with. The Stylus is great for drawing on the screen in Video Analysis apps and its performance is as good if not better than the iPhone 5S in addition to being pretty future proof from a specs perspective.
iMessage was nice since I am in a low reception house (my walls seem to destroy Verizon's signal) and run into texting issues at times, but in the end the device seemed a bit underwhelming. I am not getting that feeling form the note.
I tried the 5S for 10 days.
A few issues I did have with the iPhone 5S:
1. The Device seems extremely aggressive with Auto-Brightness. Indoors with all the window shades closed it often left the device so dim that I could barely read the screen. Using a higher Manual Brightness means the phone doesn't last as long.
2. I could not export Video from OneDrive to Camera Roll. This literally made me go HOME to my PC and email myself video files so that I could download them onto the phone.
3. There is no easy way to delete cache files (all Samsung Phones make this easy in Storage Settings - Just tap Cache and Clear it), which means apps that you viewed files in often will hold those files there... for a long time if not forever... It also bloats up the size of iCloud Backups.
4. 32 GB Note + All Google and Samsung Apps installed leaves you with something like 2GB more space out of the box than a 32 GB 5S with Apple's 1st party apps installed (iLife, iWork, iBook, Remote, Find my Friends, etc.). Something about having ~21GB space on a 32GB phone practically out of the box just felt wrong, given how much they make you pay for that extra 16GB and the lack of a MicroSD slot (which the Note has). BTW the Note numbers is with the Verizon bloatware installed (which includes basically Amazon's entire Ecosystem - I have since disabled practically all of those, though
).
5. Screen Sensitivity on the iPhone was particularly bad. This was very noticeable at the edges of the display. I had a lot of time getting into search fields and hitting buttons at the top or bottom of the display. It's as if I had to aim below buttons at the top of the screen or they wouldn't activate. This was particularly noticeable in games like Words with Friends, which frequently have you tapping in those areas (moving letters around, and the way the screen auto-zooms when you place a letter, etc.). It was driving me crazy. The Note is a breath of fresh air for gaming due to the screen size.
The Note gets about 2x the battery life of the 5s with a lot of stuff enabled, which is expected given the massively larger battery.
I heard great things about the 5S camera but found the pictures to be overprocessed. Took some pictures at the mall and faces looked like they were painted. There was clear evidence of massive amounts of processing and skin looked smudged. I find the S4/Note 3 Camera to be sharper, however the 5S is better in lower light (though the 4.4 update improves that on the S4 I heard, and could expect similar for the Note III). I have issues with a device that basically dictates that I download a third party app just to switch the camcorder to 720p. That's just not something you should need a 3rd party download for.
iPhone apps are insanely large. I'm not sure if it's because many of them are "universal," but even for a lighter user I have an issue suggesting them getting a 16GB device because I'm just not sure how well that will hold up. OneNote for iOS is like a 120MB+ download. A ton of apps were 30-60MB and used a ton of space on the device.
There were software features that I couldn't live without as well...
1. No Option to Alter Playback Speed in the Video Player, and no option to take a screen cap with on-screen button (Samsung Phones have this, and it's incredibly useful for what I do).
2. No way to rotate video player without toggling device-wide Auto-Rotation.
3. Playing Music if you skipped a song that was the only one in the album, instead of restarting that song it went to the next album, which means I was constantly taking my phone out to restart the song. Apple uses 3 presses to restart a song while Samsung uses 2. With gloves on, sometimes you're miss a press and this was a bigger issue with the iPhone than the Galaxy S3 I was using prior due to the way the iPhone jumps across Albums. With the S3, I'd just skip through all songs until it got back to the song I wanted in that album, without going to a different album (skipping 4 songs is a lot easier than skipping 100 without taking your phone out to do it manually).
4. Inconsistent Share mechanism across apps. Could not import video from OneDrive (mentioned that earlier I think). Now that OneDrive has Auto-Upload that works fabulously on Android, and I have a phone with great battery life... Things like Photo Stream suddenly do not seem that attractive and the "pull to Google+" can be ignored in Google's ecosystem
5. Not necessarily software, but viewing documents on a screen so narrow simply isn't an option for me. I was getting headaches reading that phone screen. I thought it was fatigue or whatnot, but it went away the minute I got rid of the phone. They should have gone for a traditional 4" screen similar to the ones we had with the Galaxy S devices and their kin. The current screen is just too narrow for my likes and forces content to be smaller than it needs to be. Sometimes really need to be viewed one page at a time. That's obviously not an issue on the Note 3, Lol.
EDIT: Almost forgot, but one of the most annoying things about the iPhone on Verizon was the lack of Simultaneous Voice and Data. Forget sending an email while on the phone or saying "hold a sec I'll check and see what movies are playing right now!" unless you're on WiFi. The first time an MMS failed to send I was about to run to the Verizon store cause I thought the phone was broken, then I realized that the iPhone can't do that. It was something I thought was overrated, but there's no way I'm even going to entertain a device that cannot do both at the same time.