For what it's worth, I think the kana/flick input is better overall but especially in small/low screen space situations in particular. If you have a small screen and big fingers, it can be difficult to write using an on screen qwerty keyboard. That's kinda why I prefer writing in Japanese on my cellphone instead of English, because I end up fat fingering all over the qwerty keyboard.
The 10 key system is really easy to learn once you figure it out since it's all based on the same pattern.
Top left of the 10 key is base あ.
Flick あ up to get う.
Flick あ left to get い.
Flick あ right to get え.
Flick あ down to get お.
Top right of the 10 key is base さ.
Flick さ up to get す.
Flick さ left to get し.
Flick さ right to get せ.
Flick さ down to get そ.
The above pattern also applies for か, た, な, は, ま, や, and ら.
わ is special though.
わ left gives you を.
わ up gives you ん.
わ right typically gives you ー.
わ down gives you nothing.
For Android phones, unless you get a Japanese phone, you would most likely need to download a Japanese keyboard. Simeji
and Google Japanese Input
are popular and support both modes of input.
Any Android phone should be able to install a Japanese keyboard regardless of what language the phone is in, so pick a phone that you think is good instead of what you think would have good Japanese support. For example, my old Samsung Galaxy S Vibrant and my current HTC One M7 both work perfectly with Japanese keyboards but they are from US carriers.
Note: Japanese keyboards suck at qwerty mode in general imo. They don't put an emphasis on making it easy to write English so it can be a pain to write English using the Japanese keyboard. You have to peck at each letter individually instead of swiping across the keyboard like some other keyboards designed for English.