As mentioned already, con would be the Trompowsky. Another is the Catalan can be played without an early Nf3. 1.d4 Nf6 2.c4 e6 3.g3 whereas 1.d4 d5 2.c4 e6 3.g3 allows 3...f5, so typically the Catalan players will play 3.Nf3 Nf6 and only then 4.g3. 3.Nf3 f5?? Is bad because of 4.Nc3 Nf6 5.Bf4! followed by 6.e3 and 7.Bd3 with the ideal setup against the Stonewall. That is why Stonewall players must wait for g3.
One pro is some hate the Nimzo enough that they will play 3.Nf3 if they are not Catalan players. This avoids exchange lines with Nge2. Many nimzo players play the QGD instead of QID or BID against 3.Nf3 and they will go Nimzo against 3.Nc3.
What are the pros and cons to using the Indian Defense move order for the QGD? Like 1. d4 Nf6 2. c4 e6 3. Nc3 d5