LBE and pdroid can be used together (which is interesting because pdroid doesn't block internet access). It seems pdroid is more efficient otherwise (I read several posts saying LBE doesn't stop as much as it should) and most important of all, apps don't crash when they are denied permissions, which is what sometimes happens with LBE.
I use LBE myself, and would like to install pdroid too but haven't managed to do so so far (it seems there is a problem finding a patch for MIUI?). Installation is not very easy, and that is clearly a drawback.
But I do hope to find a solution and keep both apps