You can get a PSP (phat old ones) super cheep and use CFW on it and use PSPUAE, long time since I tried it but that's handheld and it got a DPad + Buttons you need and you got a ton of other emulators and games.
Still have to release new version I have been working slowly on for the last 3 years.
Just need time to finish it off. Been working on getting HDD support working and fixing some old bugs.
Just got given a Vita, so hopefully soon, the SDK will be sorted and a native version of PSPUAE could be done.
Besides PSP, UAE4ALL2 on Android is best by far. Controls are ok, not sure why people moan unless your using a phone. On my nexus 7, it runs very well.
I run my custom 3.9 setup from my real amiga on it. Its like having my real amiga on the go.
Joymouse prog is best to use with, as then you dont have to mess with mouse.
I would also recommend "hackers keyboard" from playstore. It has all the odd keys, normal droid keyboard doesn't, meaning you can quit WHDLoad games without resetting / restarting emu.
If you get spashtop2HD setup on both your PC / LINUX machine, you can use your tablets / mobiles and run WinUAE on the go. I have done this many times while away from home. Have the perfect setup (CD32) just for tablet use.