It's far more natural feelingfor rabbits to drink from a bowl, not to mention easier for them, so yes, I've observed that rabbits with bowls will consume more water. And I do think, that having bowls as opposed to bottles in the summer, makes access to water much more manageable for rabbits.
However, water bowls can be contaminated much more easily than a bottle. Rabbits can easily urinate and deficate in them, thus destroying a fresh source of water. And if the bowl is not sturdy, they can be tipped over. The biggest problem I've seen with bowls, is that rabbits with larger dewlaps usually end up with a green bacteria build up from the moisture they are exposed to when the rabbit drinks from a bowl. This can cause some severe problems down the road if it's not treated.
The only problem I've had with bottle is that they freeze during the winter. We solve this problem by only filling the bottle half way with hot water(which also saves on water since rabbits drink much less during this season anyway), and then we can gradually add more hot water if need be to the bottles, which in turn melts the ice inside.
