My experience with Select2 was great on desktop, but on touch mobile devices greatly varied, with some quirks always present. For example, on xperia st15i with ics and stock browser dropdown was always closing itself because of keyboard stealing focus. Only way to bring it open again is to touch the menu dozens of times, hold finger for a second and other voodoo magic. Or to start typing while the dropdown list is closed, and how many users will figure this out?
Selectize.js seems to be much smoother than Select2, but it also has issues on its own on mobile for e.g. when the value is selected or inputed it moves the page all the way to the left for some reason. Also, on older Android 2.x devices which do not support overflow, it is impossible to select past the few top options, since the keyboard does not pop-up. :(
Still have to test Chosen and it might be not such a bad idea to be disabled for mobile devices after all, but in the end good old dropdown works always and everywhere.
Update: now I have also tested Chosen as well, and it is better in one area: it does not work on mobile by default (great!), but it has filtering words issues. For example, does not search in the middle of the words, and if you use   hack for aligments, it will also ignore complete options. Back to drawing board.
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– Bootlace