Sounds like the hosts file isn't being updated. You're rooted correct? Does AdAway ask to be granted root access when it's launched? Is it listed in your Super user or SuperSU app as granted?
Also, what hosts file source are you using? I just use the MVPS one (
http://winhelp2002.mvps.org/hosts.txt) and don't see ads in the browser or apps on my Note 2, OG Note 10.1 and OG Nexus 7. They're all using a 4.1.x version of Jelly Bean yet, but I wouldn't think the OS version should matter as it's just a modification to the hosts file. Also in AdAway, under "Host sources" verify the hosts file has a check mark and the date is recent.