I haven't been down the mobile road, yet, but I'm also doing some research to start the journey in a few months. jQueryUI does not support some mobile interactions, e.g., touch, drag, swipe. There are UI plug-ins to deal with (some?) of the interactions. Touch Punch is an example plug-in.
The jQuery Mobile team has stated their objective to support all of jQuery and jQueryUI.
http://jquerymobile.com/strategy/Whether that objective is completely fulfilled is hard to say, but friends of mine using jQuery Mobile have reported favorable results. In my case, it seems that getting command of "responsive design" may be a bigger issue than getting up to speed on jQuery Mobile. You have the "responsive design" learning curve no matter which road you choose.