Never been to HDDR, but based on the atmosphere I'd say park clothes are ok.
I voted for dress up mainly for Cirque. We dressed up (I wore black pants, heels, and a dressy top, DH wore a suit and tie) and we fit right in. I think if we were dressed in park clothes we would have felt severely under dressed. It also depends on the show time. I would think maybe an afternoon showing would be less dressy? It's all up to your preferences. We are people that would rather be over dressed than under dressed. Have fun! Cirque is AMAZING!!!!