Reasons I love my HTC One M8 (and my Galaxy s2 before) over my wife's iPhone5:
I've had a big phone for years now (4.7" with the S2, 5" with the One)
My One has a 1080P screen (unlike the iPhone 6's 720P screen...still haven't caught up)
swipe gestures to wake up the phone in different ways
IR blaster (handy for those times when I've misplaced the TV remote and don't want to get up to look for it right away)
Expandable Storage I have a 64GB microSD card in there right now, but it will take up to 128GB.
MicroUSB connectivity. The sheer number of cables I have from previous phones (blackberrys, samsungs, etc) that fit this phone is extraordinary. I have one at the office, one in the car, one in the bedroom, and one in the living room. And I haven't had to buy a single cable separately.
Google Maps navigation. I use it in the car. Compared to the navigation feature on my wife's iPhone5, it's worlds ahead. We use the Android nav exclusively.
Stereo Speakers on the front of the phone. They're LOUD, and I don't have to cup my hand over the back of the phone to hear anything when playing video.
A real file system. I can plug my phone into my computer and have access to the complete file system on my phone (including the Android install folders, IF I wanted to modify my OS). I can also specify where I want apps and documents/pictures to download TO on my phone, and move them around at a later date.
Honestly, I couldn't live with an Apple Phone. My wife can, but only because she uses ITunes to buy music for her work. She can just purchase and download music right on her phone, then plug it in at work to teach her class. Honestly, ITunes is the ONLY reason to buy an iPhone over an Android phone. If you're already in the Apple eco-system, it may make sense. If not, Android all the way.