The inconclusive results of the previous first-principles studies on the Sigma 3 grain boundaries (GBs) in CuInSe2 reveal the importance of employing a method that can correctly describe the electronic structure of this solar-cell material. We employ hybrid functional calculations to study the Sigma 3(112) and Sigma 3(114) GBs in CuInSe2 and CuGaSe2. The electronic structure changes introduced by the formation of GBs are threefold: the creation of gap states, a shift in band edges, and the alteration of band-gap sizes. Gap states commonly behave as recombination centers, but the band alignment and the change in the band-gap size induced by GBs mitigate the destructive effect of these states in CuInSe2. That means that S3 GBs are not detrimental for the carrier transport in devices based on CuInSe2. Conversely, these GBs are destructive for the carrier transport in CuGaSe2. The different behaviors of the Sigma 3 GBs in CISe and CGSe might be considered by experimentalists to optimize the device fabrication to achieve high-performance solar cells.