While I agree with you that the appearance of quads, especially that of Trappistes Rochefort 10, might resemble a robust stout, I cannot agree that these styles of beer are close to each other in terms of flavor.
Whereas a quad usually has a very complex flavor – quite often with notes of ripened fruit, raisins, herbs, and a has general ”wine-like classiness” – stouts are usually pronounced in roastiness, bitterness from the hops, coffee, dark chocolate and licorice. Stouts also lack the typical ”Belgian yeastiness” that is quite ubiquitous in quads. Of course, there are a ton of stout varieties and some might have notes resembling a Belgian quad.
This is my experience anyway.
Well, perhaps my palate is not terribly sophisticated, and - while I think the Belgian quads are smoother than most of the beverages marketed under the "imperial stout" label, I do think they have more in common with each other that either might gave with some of the insipid ales form the British Isles I have had - or, for that matter, than they share with some of the dreadfully underpowered - and underwhelming - porters such as Guinness.
But, each to their own.
Personally, I am a huge fan of the Belgian quad style of drink, and for consistency, and quality, there is little better to be had in winter (and those tedious days of early spring).