Those 2 lifts are pretty good choices in that range. I have read of a good mix of people that have had great success with RE and others that the lift sagged pretty quick. The lift comes pretty tall and then it settles to ride height. There are a lot of people that are happy with the BDS lift and if you want more opinions good to Jeeps Unlimited, there are a lot of guys there running BDS.
The thing that can make or break a lift though is shocks. Don't cheap out on shocks like procomps or low end ranchos, spend the money and get a good set.
I am not sure what tire size you plan on running but you will definitely have enough room for 33s, but 35s you will need more room.