If pruning a reblooming type like endless summer, I cut them off and shape the plant at the same time, trying to cut right above a node or where the stem branches to a V---as I would prune a tree etc. (Most of the time there are several browning blooms to deadhead at one time.) If I want to cut the browning flowers off a big leaf then I'm careful about it if if is after early/mid July.... Don't want to cut off any buds, so I just snip the flower heads off without pruning off really any stem of the plant.

If you leave them, they look very pretty in the winter.

I cut them off all hydrangeas, I like things tidy. On ES I cut down to right above the next node.