The first answer which comes to mind is that the Aedra, by their nature, prefer stasis. To meddle is to interrupt the stasis, to induce change. Thusly, it goes against their nature, and only in the most extreme of situations, or at least in situations they deem worthy, will they opt to interfere. The Daedra, on the other hand, love change. Seeing what happens when X occurs to Y is what drives them forward. Stasis is boring and useless to them, and so they're always looking to stir things up to feed their own whims.
The other thing to take into account is the balance of power. Both Daedra and Aedra are immortal, though I suspect this to be to a limit. Even so, they do not have an unlimited reserve of power. The Daedra, though, have a bit of an edge over the Aedra since, thanks to Lorkhan, the Aedra lost a fair bit of their power during the formation of Nirn. The Daedra simply have more energy to expend, and so can do so more wastefully and frivolously, while the Aedra have to weigh the options and consider each action with care. They can't interfere on a daily basis as it would simply drain them.
I guess it's a good question how sentient they are, though. Are they individuals, like mortals; or are they like forces of nature?
Though it is a bit off topic, my image of the et'Ada is that they are what we see in the Shivering Isles: a plane, a realm, a world of energies and beliefs. We often think of them as personified entities, like the old Scotch-Irish banker by the name of Sheogorath, but that old man is not Sheogorath; rather, the Shivering Isles are Sheogorath, the old man just being a nexus of sorts, a point akin to a tower, the axis mundi, upon which the energies of the plane are focused such that it gives the form of a conscious will with a physical body. Hence why, as Order overtook the Isles, so too was the image of Sheogorath overtaken by Order. The nexus is merely a reflection of the plane, which is the true Daedric Prince. Furthermore, this also would seem to explain what Haskill meant when he said the new Sheogorath would "grow" into his role. Truth be told, Sheogorath never died or disappeared, he merely lost control of his nexus to Jyggalag*, but now the unwitting mortal who aided Sheogorath has (un)willingly sacrificed his body to become the new nexus. In time, the forces of the Isles will bend him into the old banker we all know and love. (Mind you these are only my own fanciful theories, based on what little I've gathered over the years.)
From this point, one could see the difference between Aedra and Deadra, greater and lesser. The planes known as Aedra believe that it is stasis which must be had to preserve them; to change is to risk a return to nothingness while stasis is a denial and casting off of ones limits**. The planes called Daedra are those which feel that change is required for continued and expanded existence; to remain still is to be dead, while to change is to reach towards the limits of ones being. The greater of their respective kinds are the planes, while the lesser of their kinds are void, existing only in a bizarre state within the "waters of Oblivion" (From what I can gather, the lesser of the Aedra perished in the formation of Nirn, leaving only the weakened planes who had sacrificed just a part of themselves towards Lorkhan's goal rather than their entire being). Until summoned ashore by a plane, they have no form or being (they are the potential without sustenance), and thus must rely wholly on the patronage of a plane for sustained existence (for example, the Mazken and Aureals of the Shivering Isles).
*
Jyggalag has always baffled me as he does not seem to be the type fond of change, but rather one more aligned with the Aedra. Perhaps that is why the Daedra so bitterly opposed him, cursing him to become as they were. As a realmless entity, though, I am uncertain as to how long he can sustain himself, especially if he were to come under attack. He may have a reserve upon which to sustain himself, but without a realm, he seems to be little more than a powerful but ultimately lesser Daedra, doomed to the waters of Oblivion if he were to perish. That may explain why he surrendered to the new Sheogorath in the Shivering Isles?had the battle continued, he might have been finished, and thusly cast into the waters of Oblivion. Better to retreat and formulate a new plan than to suffer such a crushing defeat.**
Static time is also infinite time, though I'm not as certain about "pure" stasis?infinity in all directions, to be without beginning or end or any notion of confinement. An infinite series, a beginning without an end or vice versa, and true infinity, no beginning or end, are not quite one and the same. It occurs to me upon considering this point that the Aedra may, in fact, differ from the Daedra. Perhaps it is that the Aedra are beings without any confining measures?no shape or perceivable limit, no place in time, et cetera?while the Daedra are ones which have given themselves definable and perceivable limits (their realms and avatars). It is hard, if not impossible, to experience or comprehend that which is without limit or form, without existence as we commonly consider it to be. But this line of thought is only adding speculation to speculation. Best leave things as they are until new elements are introduced.