A recent discussion in comments under Alon Amit's answer prompts me to offer some reflections on quid's publicly stated feelings and judgments about MO and the differences between MO and Math.SE. I think some of this is also reflected in an interesting discussion I recently had in the MathOverflow chat room with Martin Sleziak.
For me, some of quid's feelings came strongly to the fore in a kind of argument we once had over in the meta thread on reopening closed questions, here: https://meta.mathoverflow.net/a/2564/2926. The MO question we were discussing seemed, to me, to be of obvious interest to mathematicians and really spoke for itself -- "needed no introduction" so to speak, and hence deserved to be reopened. Quid objected that the question formulation was poor, because no motivation or context was set, and I got the strong sense that for quid this is really a sine qua non for a MO question to be good. Whether this type of issue weighed strongly in quid's decision to quit MO is not for me to say, but I do consider it a data point.
Martin Sleziak in our discussion (which got started round about here: https://chat.stackexchange.com/rooms/9369/conversation/discussion-about-differences-between-mo-and-math-se) raised my consciousness about some significant cultural differences between the two sites (I am only an occasional participant over there). It seems that one important ethos at Math.SE is to consciously create a repository of knowledge, which may involve a conscious effort to "tune" a question so that it is not just about the questioner's immediate concerns, but includes an explanation for everyone out there that places the question broadly within mathematics and underlines its possible significance. This is obviously related to quid's line of argument at the reopening thread mentioned above. According to this ethos, answers too at Math.SE should not be directed just to the questioner (e.g. his/her current state of knowledge), but metaphorically over the head to address the wider audience out there, again with a conscious view to build a knowledge data base.
Here at MO, questions are by and large accepted based on perceived level, either as being obviously a question a research mathematician might need to ask, or as posing a challenging problem for research mathematicians. (For an example of the latter, recall Is the sum of digits of $3^{1000}$ divisible by $7$? -- clearly this was not a question asked by a research mathematician, but it was accepted anyway as posing a curious challenge -- I for one thought about it for ten minutes or so.) In either case questions are generally accepted on their own merits, and there is generally not a concerted effort to tune questions further to explain their broader significance unless it's really not obvious to users what their point might be. (Yes, it's true that in Help we say that the setting out context and/or motivation helps make a question good, but certainly at MO that's not "enforced", or only very laxly so.) And it may be true that answers at MO are usually more in view of helping the individual questioner than of speaking to the audience out there and for the ages, so to speak -- this was also touched on in the discussion with Martin.
I wouldn't say either mode is "good" or "bad" -- MO and Math.SE are just very different beasts and appeal in different ways to different audiences. Here at MO, our quality control is mainly based on level as described above, and otherwise it's largely live and let live, granting authors a certain degree of autonomy in how they choose to ask questions. The result is that MO is a garden of limitless delight for a sophisticated audience, but maybe somewhat loosely organized (which I believe quid also publicly commented on, but I'd have to search to find it). Over at Math.SE, a different kind of quality control is called for, and I expect there is more vigorous hands-on editorship over there over question formulation.
From the very get-go leading up to the move to join the SE network, MathOverflow has in spirit always wanted to maintain its autonomy and independence (befitting broad cultural norms of professional mathematics communities, I think): recall the discussions we've had about opting out of the network should the SE hand be felt too heavily. There is a certain level of acceptance here of the wisdom of certain SE operating principles, but I don't think we're quite as beholden to those as some of the other SE sites. Math.SE on the other hand strikes me as operating more according to the "SE book", which quid certainly seems to have mastered.
I would like to congratulate our gone but far from forgotten user quid on being elected as a moderator at Math.SE (congratulations also go to Jack D'Aurizio). I have no doubt he/she will be very thorough and conscientious; being virtually nonpareil in his/her knowledge of SE operations, he/she will bring that knowledge to bear effectively in his/her moderator duties.
Postscript: some more thoughts by quid are here: https://chat.stackexchange.com/rooms/9369/conversation/more-remarks-by-quid-on-his-mo-account-deletion
