I have both brands of water bottles(as I am an avid water drinker and for some reason prefer drinking from a water bottle) the bobble does not wash well in the dishwasher. It warped and I was very disappointed. The Brita has never had an issue. It's easier to squeeze and drink from. Also size wise it's a little more water :)
My roommate had the Bobble and I had my Brita, and the weirdest difference was the silly noise hers made every time she drank from it! The Brita bottle was also more conducive to using during sports, as the top is connected and the stream from the cap is faster than the stream from the cap of the Bobble.
There are pros and cons to both! I hate how flemsy the bobble water bottle is but I think that the water tastes so much better! When it comes to the Brita, the water has a funky taste and you have to suck a lot to get a descent amount of water.