the best app API is HTML5.
you can store data like parse.com for free with a google spreadsheet.
they seem to be targeting native apps.
unless you need ultra-responsive UI for a game, you can probably build the same app using html5.
there are a million frameworks out there, from low-level jQuery to high-level abstractions like polyfills for <audio>, drawing APIs like processing and raphael, and semi-automatic data binding like knockout.js.
what's the best?
it all depends on what app you're building.
what's the best tire size for a vehicle?
BROWSER STATS [% share]
(2013/10/31) IE7:0.5, IE8:8.6, IE9:5.3, IE10:12.3, FF:17.7, CH:41.8, SF:8.1, MOBILE:20.4