Why have a big brain weighing you down when all you do is fly long distances? It is proven that migratory birds and bats have smaller brains than birds and bats that are sedentary (stay in one location all year) because a large brain becomes energetically inefficient during migration.
The bats that are sedentary need a larger brain to be able to adapt to its varying habit that they keep to during the year. They need the ability to behaviorally change and react to the surroundings and since they are not flying any kind of extrenuous distances to a more favorable habitat, having the heavier and larger brain is a cost they can pay. Having the ability to behaviorally change will include being able to forage for different foods and to physically meet the needs of the weather around them. It is quite the opposite for the migratory bats.
These migratory bats can not afford to have the larger brains because brains are heavy and energetically expensive and these costs do not make it practical for migrating bats to have large brains. The cost of migration is not met energetically with a large brain and vice versa for having a large brain and trying to migrate. Along with overall brain size, the size of the hippocampus and the size of neocortices were also taken into account.
When the results were addressed, and it was concluded that migratory bats had overall smaller brains and also smaller neocortices but a relativiely same sized hippocampus. Interesting enough however, the body masses of the two did not differ hardly at all. This even further supports the thought of the energy trade-offs. The bat that travels more extensive distances will need more muscle and better endurance, which this would increase its body mass, just as the larger brain would increase the mass of sedentary bats.