2.0 will eventually become the best option since it doesn't support IE 6, 7 and 8, this makes jQuery much lighter and could possibly bring better performance.
Right now jquery mobile doesn't fully support 2.0, I'm having issues replacing 1.9 with 2.0 on my projects - the new slide panel seems to still need some work to get it up to 2.0 standards.
I would keep using 1.9 for now and keeping an eye on 2.0 support for jquery mobile, hopefully the team releases a new version soon.