Although I'm a big fan of Android for most purposes, Android is not really there when it comes to applications for live music performance.
The Android music apps that do exist suffer from latency problems. I believe these are caused by a combination of the Android OS not having music as a design goal, and of the broad range of hardware platforms it runs on.
So the bad news if you're an Android fan, is that iOS is the place to be for music apps. The good news is that you can probably get away with a couple of generations old, used iPad.
For looping on iOS, there is an excellent app called Loopy. It will work with headphones and the built-in mic. But for high quality results, you probably want to invest in an audio interface for your iPad. This would allow you to use an XLR microphone.
Having said all I have about Android -- things are changing. Android is now compatible with USB audio interfaces, and there is an app which clones Loopy - it's called "Looper". You'll still find that, for now at least, there is a much greater choice of musical apps on iOS. But you could try Android and Looper to see if it works for you.