The common thread I'm seeing here is the primacy of the combat pillar in 4E. It is a fact that A, E, and D are all attack powers, and I can see how a repeated focus on combat over several game sessions can make the play experience seem samey.
I have a conjecture about this that I'm happy to share.
As far as I can tell (from reading modules, and reading threads, seeing how people describe their play) the default appproach to D&D is highly GM-driven, where the fundamental job of the players is to work out what the story is that the GM has established but not simply revealed to them, and then to follow clues/leads that come out of their emerging knowledge so as to make the right choices that will lead to the conclusion.
In this sort of play, combat is not usually a device for driving "the story" forward, because it usually does not involve
working anything out about the story the GM has established.
My own view is that 4e D&D is
extremely ill-suited to this style of RPGing. Its high degree of player "empowerment" (eg say "yes"-type play, player-authored quests, etc) pushes against tight GM control over the plot. And its emphasis on combat as a pre-eminent mode of conflict resolution begs for combat to be a, perhaps
the, primary mode of driving "the story" forward. (For a good model of how this can work, see any Marvel comic from c 1970 to c 1990; ot a number of REH Conan stories, though comics are better models for D&D because of the team aspect in many of them.) This is just one reason why I agree with
@Zardnaar that "4E couldn't be played like 3.5 no matter how hard you tried."
4e has U and vastly impactful skills and SC ...so I say meh to 5es other pillar purported emphasis.
With fairly solid skill system, support for skill challenges, and less arbitrary "I win" capabilities restricted to only specific classes, I would ask rather what 5e should learn from 4e in that respect.
I agree with these points - one reason I have little interest in 5e D&D is that I don't think it offers very much for out-of-combat resolution. In my view 4e D&D is the best version of D&D for this.
But I still think it's the case that, in 4e, the
pre-eminent mode of combat resolution is combat. This is manifested in PC stat blocks (not all combat, but it's the biggest thing), NPC and monster stat blocks (the same), not to mention the general thrust of the default fiction (ancient wars, epic struggles, etc).
And yes, I'm aware that attack powers can - as hinted at in the DMG, and further elaborated in the DMG2 - be used to modify skill checks in various ways. That's been a common feature of my 4e play, though I think my group is probably atypical in this respect. (We also see a lot of ritual use, which seems to be atypical.) And I'm not saying it would be
impossible to run a 4e game that was overwhelmingly non-combat conflict resolved via skill challenges. But at that point, I personally would be wondering why we're not playing HeroQuest revised instead.
Given all this, I think it's a pity that the 4e DMG has lots of (very good) advice about the technical/mechanical aspects of combat encounter design, but has very little useful to say about how to use combat encounters as drivers of an unfolding fiction. (The Worlds and Monsters preview volume was better at this than the DMG, but still not excellent.)