Aperture always wins for me. I have a variety of refractors going up to 140mm APO, as well as dobs going up to 16" with a premium optic. My refractors can show better contrast on most objects at low-mid power... but my dobs, after 10", really start walking away from the refractors in terms of overall performance and will always show more. Under 10" and cooldown is fairly quick for me with dobs. Even in average seeing, there are always moments where the air is stable enough for a fraction of a second to glimpse spectacular detail with a big dob. Lucky imagers count on those moments of good seeing, as do visual observers. SCT is the only design where its long thermal acclimation really hindered my ability to use it on a variety of objects after setup.
That said, I love all telescopes and love the differences in their designs. Just because my big dobs can usually wipe the floor with the refractors doesn't necessarily mean I undervalue them or use them less. Being under the skies with any scope is better than none, so I enjoy any chance I get to bring out a "toy". It's a privilege to be able to enjoy and appreciate these kinds of instruments.
I think that a telescope's limiting magnitude and seeing could also be a good overall performance indicator. There are so many factors when making an observation, including central obstructions. I had a good lesson on seeing and thermal acclimation when I challenged myself to observe Triton for the first time, across a series of nights with a 12" dob. For the first couple of nights, with just average seeing, I could swear I could see it periodically shift in and out of view with averted vision at around 400X....but I learned as I performed my observations later in the night on subsequent days, that my scope's thermal acclimation was also a significant factor. With my scope cooled down a bit better and by using my boundary layer fans, I could get a steady view of the faint moon without using averted vision. I'd like to try that exercise again with my larger refractor, where its limiting magnitude is less than the big dob, but still within the realm of the refractor's capabilities. I think the lack of a central obstruction will help me to see it, but I anticipate it will again be a unique challenge, where acclimation, seeing, aperture, telescope design, and observer experience will heavily factor in my success. Regardless of the outcome, I'm sure I'll walk away having learned something new.