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In my humble opinion, if the mirror of a 10" f/5 dob is still spotlessly clean and freshly re-surfaced, it should perform more or less on par with a 6"-6.5" Apo in terms of light-gathering ability ONLY, the image quality will not be in the same league.
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This isn't right. A 10" mirror gathers 2.37 times as much light as a 6.5" lens and even allowing for lower transmission off mirrors and the secondary obstruction the 10" is still going to be considerably superior in light-gathering.
As others have said a lot of comparisons people make refractor v reflector is expensive APO v generic Chinese reflector. If you get an equivalent quality reflector it's going to be a lot fairer comparison.
To give an illustration, my 10" Mewlon has two mirrors and is a pretty decent quality folded reflector. Once it is properly collimated and cooled, and provided the seeing is decent, it will absolutely crush my 5" APO on DSO's and planets. The difference on something like Eta Carina is like night and day, the Mewlon can deliver larger image scale and a much brighter image.