I would say if possible to keep the bag on Delta metal, it might be wise. I once had a cancellation at the gate and a rebook flying the Friendly Skies. The bag transfer from Delta to UA was mishandled and my bags didn't arrive. While UA was responsible for the bags as the carrier flying me, they weren't all too helpful. I'm not sure how "responsibility" for bags getting there works when you are traveling on multiple airlines--who is ultimately responsible (and supposed to handle your baggage claim if lost)?