Disclaimer: I am here to discuss ideas, not to "win" anybody over. This post is not in response to any person in particular.
First, it's possible to overstate the mechanical differences between the 3E treatment of skills and the 4E treatment of skills. Suppose I'm a DM, and my story involves a PC running down steep stairs. If I turn to 3.5E DMG page 31, I see that this task is one of the examples for a DC 10 skill check, appropriate for a 1st-level rogue. If I turn to 4E DMG page 42, I see a table listing easy, moderate, and hard DCs by level. If my PCs are 1st level, I might conclude that running down the stairs is a moderate task (DC 10 with errata). If they are 10th level, I might conclude that it is easy (DC 10 with errata). If they are 20th level, I might conclude that it is trivial and not bother checking the table. My advice to unwilling converts stuck playing 4E is to pretend that the table includes two more columns, one for trivial (epic heroes at the tavern's back door) and one for impossible (rookies finding Vecna's lock). Page 42 says to choose the DC depending on the attempted action's difficulty. Nowhere does it say to determine the obstacle depending on a presumed probability of success.
That said, it's possible to understate the philosophical differences between the 3E and 4E treatments. The 3.5E DMG page 31 lists concrete examples, their DC, and for whom the example is an appropriate challenge. The 4E DMG page 42 lists DCs by level for abstract (relativized) difficulties: easy, moderate, and hard. The former is a "world-centric" approach; the latter is a "PC-centric" approach. It's clearly possible to be more comfortable with one over the other.
Personally, I am a big fan of 4E. That said, I do find that it's simplistic to say that 4E is "easier to DM." I would say that it's more freeform. For people who are good at making judgement calls without much guidance, such as so-and-so task would be "easy" or "hard" for a character of X level, perhaps it's liberating. As a new DM who is still learning how to improvise, I sometimes crave more structure. Okay, sure, I should litter my battlefield with terrain that involves level-appropriate skill checks to foster an engaging encounter. So what terrain would that be?
Finally, I can certainly sympathize with a fan of 3E who worries that their DM is taking an extreme approach to page 42 and is making every skill check they encounter a 50-50 shot, instead of devising their own story and using to the rules to run it. I would agree that page 42 could be more clear. I suspect it fails to communicate the designers' intent, in much the same way that we know that the original presentation of skill challenges deviates from the designers' intent.