Composite vs Prime Order Groups in Attribute Based Encryption
Composite-order groups for pairings are sometimes a necessary tool provide a proof for adaptive security. Most schemes for prime-order groups only reach selective security in their respective security models.

While the security generally increases, the performance of composite-order group pairings decreases heavily. Compare prime-order pairings of Type A with composite-order pairings of Type A1 here. All operations for Type A1 take roughly 18 times as much time as operations for Type A (although, they have different Dlog security levels, but that doesn't influence as much).

Dual Pairing Vector Spaces (over prime-order groups) behave similar to composite-order pairings in that they enable more powerful security proofs, but perform roughly 10 times slower than basic prime-order pairings.