I don't have a One, but I do sync my Android phone with iTunes.
I'll put my vote in for iSyncr. There is software you have to install on your PC, but it allows you to keep all of your music in iTunes without needing a separate music manager. If that's important to you then iSyncr is the best option I've found. If you use Rocket Player you have a bunch of options that you don't really get with other music managers and iTunes. For example you can keep your played counts and make and change playlists on your phone and sync those back to iTunes with iSyncr and Rocket Player. I'm not sure you'll get stuff like that with DoubleTwist or Google Music.
You don't need Rocket Player for it, but you can also sync songs you buy on Amazon back into iTunes from you phone, which is nice. You can also sync automatically over WiFi so you don't need to plug your phone into your computer. If you use Tasker (more about that later) the options you have on how to control when that sync are done are almost limitless. If you are OK with changing what your main music manager is (I actually wish I could do that) then this might not be the best option, though. It's nice if you have other iDevices that you want to sync to not have to keep your music managers in sync as well as your devices.
Note that no matter what method you use you'll have to find a way to strip the DRM off of music you bought through iTunes before April (?) of 2009.
If you like tinkering then Android will blow your mind. If you like changing how things look then check out:
Beautiful Android Themes, Wallpapers, and Homescreens
AFAIK, rooting isn't required for a vast majority, if not all, of those themes people have made.You might have to spend $4 on a new launcher and buy an icon pack, but those are reusable and that's only if you're really picky about how everything looks. You can do a lot with free applications (i.e. Nova or Apex).
If you like changing how your phone works, Tasker is the reason to move to Android. Here's the best set of articles I've found:
Overview of Pocketables Tasker articles
It has a bit of a learning curve, especially if you don't have any background in software programming, but the things you can accomplish with it are crazy. You can add custom functions to the voice assistant. I have mine search my IMDB app directly if I want or speaking (and copying to my clipboard) the address of my current location. I can also save, navigate to or just show custom locations in Maps. I have an Android tablet, too and I have a widget that displays the battery level of it and whether or not it's charging. I even have a voice command on my phone that reports what app is being used on the tablet. I can also control things like ringer volume, account synching and which features are on or off (WiFi, GPS, Bluetooth, etc) based on location, time, WiFi activity or just about anything else. I even have one that puts up a persistent (I can't get rid of it) notification if I'm at work late and gives me three options on what to automatically text my wife. It only goes away if I leave work.
It's just a great way to add totally unique and custom functionality that you almost certainly won't get from apps alone.