I'm actually switching from an iPhone 6 to a Nexus 6P tomorrow. The main reason I'm switching is due to the cost (iPhones are quite expensive in comparison) but my phone uses are much more different than you. I also like that I'll get a better screen, more battery life and more storage for much cheaper than what it would cost for me to move from a 6 to a 6S plus. I've used Android in the past (Nexus 7 until it was dropped and the screen shattered) but I haven't used it as a daily driver as a phone. I do like Android a lot (but also like iOS) and also have access to an iPad mini, so I'll have both iOS and Android. I think the thing is, if you really want to make the switch you have to dive right in and not think about it. For me the biggest loss will be iMessage but you don't mention this as one of your main uses so for phone calls/music I think you'll be fine. Are you having issues with your iPhone? The 5S is still a good phone.
Could you please elaborate on how it's been a nightmare for you? I'm just curious as I'm switching to Android. But I'm not heavily invested in the Apple ecosystem, I've only bought 1 app that I can remember (1Password, love it!) and they have an Android app I can use.