I guess the main problem is when universities, employers, etc. require that you install an app for access to some essential part of your business with them. That's the kind of application that cannot easily be replaced with an open source equivalent, and will unfortunately probably tie many to proprietary versions of Android in the near future.
Some of the time using these apps can be avoided, but I'd imagine this is only temporary, and either way it adds significant inconvenience a lot of the time to try to go without them.
Well, I prefer Arch, but a major factor in that preference is the fact that some software I rely on for my work is very hard to find on other distributions and that creates unnecessary hassle for me.
Fedora and Debian/Ubuntu are both pretty solid choices for a base OS, but Fedora might be more robust in the long run.