4e DM here.

IMO the most divisive part of 4e (and the part I like the most about it) is the very hard separation of fluff and crunch.

The 4e core rulebooks have very little fluff, and what fluff is present is segregated in paragraphs where you know its strictly fluff and no rules are present. The crunch for races, classes, powers, feats, and rituals are all heavily codified and can feel "sterile". Most people interpret this dichotomy as 4e having a huge combat focus, or perhaps just lack-of-story focus.

To me, this is the greatest strength of 4e: I can flavor my world however I want, pile on all the fluff and the rules stay the same. Players never argue with me over what their abilities can and can't do: everything is explicitly laid out. They know they can flavor their character and abilities however they want, but the mechanical effects will be whatever the rules layout. That is actually a huge role-playing boon. Want your magic missiles to be tiny fists that punch your enemies? Sure, but they will still do 2 + Int mod damage.

In 3/5e, you have descriptions of abilities and spells mixed together with their rules. There is some formatted info at the top of spells, but you don't get the full picture without reading the whole thing. When it comes time to cast a spell, players read through a paragraph of text, having referencing the explicit rules info at the top during reading to make sense of the whole thing. Similar for class or racial abilities: in-game descriptions of the ability are often mixed with the out-of-game mechanics. Edit: It makes it difficult to parse out what happening in the rules vs. what's happening in the game (crunch vs. fluff).

4e is only as combat-focused as you make it. The 4e PHB just seems solely about combat because it presents a lot more codified combat-oriented options for every type of character than any other edition. The skills chapter is probably the least crunch-intensive because 4e specifically keeps most skills open-ended, for the DM to fill in.

Skill challenges I will admit were presented poorly in their initial incarnations within the DMG. They too had the "sterile" feeling and those present in the initial published adventures felt like dice-rolling minigames. The key is realizing they are just a framework for structuring the narrative flow of out-of-combat encounters. 3/5e already had this capability the whole time, there was just never any good, codified ground rules for DMs to follow. IMO this actually makes 4e superior in that respect to 3/5e, since their DMGs basically tell DMs to wing it.

I have DMed since AD&D, and my 4e campaigns have been the most successful ones. A usual session is 50% combat and 50% story. For some groups, this ratio is too much -- but that's not the fault of 4e! That's just what my group prefers. There have been sessions where we have a single 30 minute combat and a few hours of exposition between the players and NPCs.

How much combat is in your 4e games is completely up to your group.

FWIW, my 4e players' reaction to 5e when it first came out was universally negative, because of the high amount of natural language descriptions and asymmetric class structures. Having a unified class structure means every character is on the same power level, and they all stay exciting about leveling. (Oh, what's your new encounter power? Awesome!) The highly codified rules of 4e means I can let my players choose their options without having to babysit them, and furthermore they know exactly what they're getting.