Here's a thing, sometimes a DSO can be too bright. If it has bright areas, that can spoil your sensitivity to fainter areas, similar to a bright star beside a fainter object.
With globulars a bright centre can interfere with seeing fainter stars as you move outwards. For M13 in particular, I can see stars at the centre, dark lanes as well as outer detail in my 12". While I am very happy with that, I am curious how much brighter and more detail a 14" or 16" would show. M13 is my test DSO and overall favourite, I have recently added another 12" F5 to my Dobs flock.
But with a smaller aperture all the stars will dim, which I suspect would offset (some of/all of/more than?) the gain in dark adaptation. No free lunch?