I have purchased from both. I have an REI in town, so have purchased more from REI. I DO try to frequent the locally owned outdoor shops as well.
It depends on what gear you are talking about. REI does sell plenty of other brands (i.e. Pearl Izumi) that cover their weaker points. If I was looking for a tent, for example, I would look much farther than only LL Bean or REI brands. Although, you might end up with one of their tents, neither REI or LL Bean do much ground breaking gear development...
Enjoy the process.
S