If you play mobile rhythm games

Preferably get an iPhone. They just work. No, really.

If you must get Android (e.g. because of headphone jack), take note that a good chunk of them have issues such as note drops, ghost touches and audio latency that can affect your gameplay and enjoyment. The latter cannot be as easily mitigated on Android other than through offset settings due to how Android processes sounds, but the former two can to some extent, if the problem is not too serious.

If you hold the device in your hand (e.g. thumb players), the priority is as follows:

1. Build quality of screen (a hard glass screen protector can help to some extent)
2. Build quality of device as a whole (a thick case can help to some extent)
3. "Cleanness" of ROM i.e. how little bloatware it has; the less the better (custom ROMs can help to some extent)

If you put the device on the floor (e.g. multi-finger players), the priority is as follows:
1. Build quality of screen
2. "Cleanness" of ROM
3. Build quality of device as a whole

The screen refresh rate matters somewhat if you're more of a visual type of player, but in any case the touch sampling rate is far more important. For rhythm games with flicks, pixel density also matters as rhythm games generally detect a flick when the finger or thumb has moved a distance of a certain number of pixels, so for example the Xperia 1 series would probably be among the best for that.

As with other genres of games the SoC is obviously also a factor, but you also want a phone that doesn't overheat easily when gaming, because that causes visual and input lag and also causes dropped notes to occur a lot more often (and also accelerates burn in on OLED screens, but that's another matter) so it's hard for me to recommend devices with SD888/888+/8G1.

Obviously phones would generally be better for the former and tablets would generally be better for the latter, but there are exceptions (e.g. MiniWheatDuo is a thumb player who uses an iPad).

Other factors like limited offset options and tap area window depend on the games themselves rather than the device, so they aren't relevant when recommending phones.