DH is a Mainer and must buy from LL Bean whenever he needs new everyday items. He gets his favorite everything there, year after year. It doesn't change much.
REI is more convenient to us on the west coast though, if we want to go to a bricks-and-mortar location and kick the tires. Both are good companies. In our case, either way we are supporting the local economies of places that we love.
Sarahkonamojo is right, the store-brand stuff in both cases might not be cutting edge. But it will be solid, and good value. I don't get out as much as I would like anymore, so in the rare occasion that I need new gear I've been quite happy with store brands. My experience is that REI might have a little more selection in terms of different brands available.
It depends on what you need and how you want to spend your dollars. You'll pay more for certain brands, for titanium or other ultra-light technologies.
IMHO if you are outfitting yourself for backpacking it's important to be able to try on the gear. A pack should fit properly, and a good store will have a selection for you to try on and sandbags to put in it so you can see what it feels like when it's loaded. Same with sleeping bags. They come in different sizes and cuts now, so if you can go to a store and try them out I would do that rather than purchase online.
2014 Bobbin Bramble / Brooks B67
2008 Rodriguez Rainier Mirage / Terry Butterfly Tri Gel
2007 Dahon Speed Pro TT / Biologic Velvet