I find this so interesting, because I see 4e as much more codified (the power system), shifting away from a more free-form DM fiat zone, which is how I perceive 3.5.
Perfect example of YMMV, that.
Indeed!
Here's a few ways how it occurs for me and my group:
A - DM stuff doesn't have to follow how PCs are built/put together. This is especially noticeable with NPCs and monster design. If you want a monster or PC to be able to do XYZ, then they can do XYZ, it doesn’t have to tap into the same/existing grapple ruleset, or ply of the same spells the PC have access to, or use someother existing mechanic. This then extends to traps, terrain, magical effects, etc. Much more DM freedom.
How this has shown up in play for us is that when weird thing W happens, the players react to weird thing W rather than wonder what mechanic was used, if it was used properly, if the DM is trying to screw them over by bending the mechanic, and what countermeasures they have against the mechanic (as opposed to responding to and/or countering the weird thing happening in front of them in the world).
B – Framework and guidelines on page 42 of the DMG that says “let them try it, even weird combat maneuvers, here’s some basics to adjudicate it.” Similarly, with the explicit rule design of exceptions overriding the baseline you can design anywhichwayweird things. DM fiat can abound here.
C – In a very 1e move, re-relegating non-encounter PC abilities to not being in the ruleset has allowed some groups and PCs much greater flexibility on their background abilities.* DM has to adjudicate this. Consolidation of skills has allowed characters to be more broadly skillful and thus do more rather than hitting skill point roadblocks.
* This is one change I’m not satisfied with; while I like that background abilities no longer vie for precious skill points with adventuring abilities, complete removal left a void to me. (Which is why I wrote a background skill/trades system for RPGnow)
D – A move towards effects-based power system is more implicit in allowing players to define what their powers are and how they work in the world. Also, making the character classes more about a power/combat shtick while dispensing of some of the other non-combat trappings can allow for more freedom of character concept. (I think they could have even gone farther with this, or at least been more explicit about it) (this one is less about DM fiat, more about RP)
E – Some of the more heavily DM-adjudicated spells have largely been turned into rituals, leading for an easier time to create more (without having to worry how they fit into a combat spell structure). Plus it's easy to make special rituals for special situations, or use only by the baddies.
So, overall, these changes have let the RP flow more freely with the system being in the background for most of our game time. As a DM I'm freer to come up with what I want, even on the fly, and have it work, work well and be accepted fictionally as well as mechanically.
Combat I'd say is mostly the same RP wise, a bit more here, a bit less there, albeit with much greater movement and tactics as the combat system permits greater fluidity and ability by certain roles.
With 1Ed and similar systems, it was binary: if you chose to be a musician, you were skilled enough to be notable. Everyone else was essentially a scrub or newb.
IIRC in 1e, until the Dungeoneer’s and Wilderness survival guides there were no secondary skills (or skills at all, for that matter), it was all up to your background and the DM playing off of that if they wanted to. Or if you were an Elf. Then you saw everything, perception be darned. (kidding!

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Anyway, as stated above I’m with you on this one, I consider the complete removal of non-adventuring skills/etc as a loss for the game.
Oh, it is performance. But I'd really rather not have the most important part of it be how high the player rolls on a d20 always using the same base number. I'd far rather a skill challenge using:
I like this a lot, and I find it a great example of a skill challenge to boot! I’d use something like this too, in conjunction with what’s in my trades skill system, for such an epic battle of the bands, coupled with (actually preceded by and interspersed with) RP from the players about the whole thing.
(Epic battle of the bands… an episode of Reboot comes to mind

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peace,
Kannik