I played primarily with Adidas for years, and have played both Babolat and Nike. My take...
Babolat - I had a pair of their lower line shoes, the Team All Court III's, and they wore well, but the forefoot really lacked stability. Quality was fine, so was durability, but the forefoot instability, and comments that the Propulse 2 and 3 both suffer the same thing, have kept me from experimenting with Babolat further.
Nike - I'm on my second pair of CB 3.3's, and I really like the shoe. My foot is locked in. They've also been more durable than Barricade 2's or 6's for me, but I think that stems from the only beef I have with the shoe. The tread design is clearly built for wear, and I find Adidas shoes (B2, B6, the CC Genius 1 and 2) to have much better traction with their herringbone pattern.
After this pair of CB 3.3's are worn through, I think I'll avoid Nike's durability shoes. I'm going back to Barricades, probably the B7.
No one in this marketplace is making bad shoes. Some are more durable, and some are a better fit for some players than others. Nike and Babolat make fine products in my eyes, other than the flaws I've identified which are sending me back to Adidas, or perhaps to the latest Lotto offering which is garnering solid feedback. As always, YMMV.
I have come to the conclusion that I simply don't know what I don't know.