I made the switch from the iPhone 3GS to the Galaxy Nexus a little more than a year ago. Being able to customize the phone's interface to match what I care about is awesome. Widgets, multiple homescreens, having what I want at a glance, and what I might care about just a gesture away, is awesome. But all the other things, like NFC? I could honestly care less about. All the switch from iOS to Android has done for me is that it's made it quicker to do the things I use smartphones for, and I don't really use smartphones for much. A lot of this sounds negative. Don't get me wrong, I'm personally glad I made the switch. But at least temper your expectations with the fact that you'll ultimately be using a different smartphone. If you have a friend with an Android, play around with it.
Regarding iTunes, you don't need to move everything over to Google Play. As long as your iTunes songs don't have DRM on them, and most recent downloads don't, you can just copy them over to your phone. Google Play, and alternatively, Amazon MP3, are convenient in that they let you stream your entire library from the Internet. But you don't need to use them. You can still keep all your music on your phone.
Hardware-wise, the Galaxy S4 should be the phone to beat. The line is popular enough that people will be making custom ROMs for it anyway, if that's a thing you're interested in. Nexuses (Nexii?) have traditionally not been as powerful as far as the specs sheets are concerned, but they're also ridiculously easy to root and/or develop for. And if the Nexus 4 is anything to go by, all future Nexus phones should be unlocked. If you're a frequent traveler, this might be appealing.
I can't think of any serious pitfalls. You'd be moving from the iOS ecosystem to the Android ecosystem, so there's the obvious things like not being able to use iTunes (the iOS app, not the desktop app), everything associated with iCloud, or being able to run your downloaded apps. But that's about it.
I did forget to point out two of the more annoying things during my transition:
- A phone running stock Android doesn't have a voicemail app integrated with the phone app. I use Google Voice, but if I didn't, it'd go straight to Verizon's voicemail service, which you have to call to access. Instead of being able to see things straight from the phone app, which Google Voice allows and which iOS's phone app does out of the box. There's an emphasis here on "stock Android," since most carriers will probably put something on the phone to deal with this.
- I had to transfer contacts manually. At the time, there was no easy way to transfer iCloud contacts to Google. I don't know if there is now, and there may be workarounds, but this was annoying.
Again, my smartphone usage is pretty limited in scope. If there are apps you need to do whatever it is you do, go over to Google Play and make sure there's an Android version, or something comparable. Instagram is the notable example, since it wasn't available on Android for the longest time. It's not something I use, but if that was something you needed, a year or two ago, that'd be a significant point against making the switch.
I don't know if switching to an Android phone will solve any of the annoyance factors you have. It has been and still seems like a "pick your poison" where one offers a tightly controlled system that works very well if you stay in the box but only in the box while the other is Wild Wild West where stuff may work or may not and you might be able to make it work or maybe not.
I have a Galaxy Note 2 and it is amazing, so I would recommend that or the S4. As for moving over your itunes, you don't really need to copy them to your phone... instead upload them to Google Music and you'll be able to stream all of your music from anywhere and it uses practically zero space on your phone, plus you can access it from any computer. They allow you to upload up to 20,000 songs for free.
The only thing you would lose in the switch are any apps you bought through itunes. But at least Android gives you more choices for marketplaces such as Google Play and the Amazon App store. Plus Humble Bundle puts out a lot of Android bundles the past year so you can get a lot of cool games on that for cheap (and also gives you steam codes).
"But, I don't have any real experience with Android phones"
I don't consider myself incredibly tech-savvy, especially when it comes to smart phones. That said, I went from a BB Bold to a Galaxy S III and learned top to bottom: the phone, ice cream sandwich, then Jelly Bean in less than a few hours. It actually felt a lot more user friendly than my BB. Your reason for wanting to switch is the exact reason I chose the Galaxy over an iPhone. Although, I'm not sure I'd do it if I already owned an iPhone. Hefty price for some freedom.
I love Android but I've grown sick and tired of iOS people switching and becoming annoyed at small quirks that Android has the iOS doesn't. So, despite the fact I think Android superior I'm going to tell you reasons now to just tough it out your Android friends don't have to deal with your complaining.
1. Games. If you play games on your phone then iOS is the way to go. The games come out their first and I hear they're usually the best.
2. Apps. I know that iOS is currently struggling to keep up with new and existing features that Android currently has but when it comes to 3rd party apps iOS is king. Things like Snapchat, Vine, Instagram, and a lot of other new apps come out their first and usually have features the Android version might not get for months. For instance you can't send videos in the Android version of Snapchat.
3. Ease of use. I think this is a bullshit reason seeing as how I've gotten asked more times to help someone with their iOS device than Android but Apple says there product is easier to use so take them at their word.
4. Apple Ecosystem. Buy an iPad, an Apple TV and whatever else they've got coming out so you can fall more in love with iOS. Even though most of that cloud stuff existed in Android before Apple decided to make a big deal of it and they allegedly do it better. So instead of buying an Android phone buy an iPad.
5. Music. I think iOS has more? I dunno. Google has an iTunes match like thing that allows you to put your entire music collection on their service so you can stream it for free but Apple's is probably better. So you want to use that instead.
6. Smarter. iOS users are better than Android users. Do you really want to give that up.
7. Features. iOS adds more new stuff in each new version of iOS than Android. Since almost all those features are stuff that was already in Android plus new things they've though about themselves you get more bang every year.
@mtcantor: Android had substantial compatibility issues from phone to phone (hardware and software framentation). And customization is not really all that amazing, beyond UI apps and the like having a more free hand. I'm having trouble seeing a jump in UI experience over iOS, even if it is probably equivalent at least with 4.2.2.
I personally use android and do not want to switch (using a Nexus 4 to avoid the carrier garbage software - another significant android issue on some of the phones). But for the items you have an issue with, I would have a lot of trouble saying your going to see any significant improvement with a change. Generally android phones come out with features before apple, but those things do not usually work super well right out of the gate (the next iphone probably gets NFC + wireless charging + facial recognition since those seem to work on android now).
The reason to switch to android is more to do with wanting things like form factor (larger than 4" screen, higher res), cheap off contract devices (350ish Nexus 4), or specific hardware characteristics that iOS is not getting you (unless a particular android UI version strikes your fancy). And for the concern given to iOS update issues, at least your device is getting them. Android is getting better, but historically only directly purchase from google (no subsidy.....) type nexus devices have long term support.... but then you get no LTE.