4e has examples of what certain DC's mean... while not as exhaustive as 3e it still locks in a chunk of that color to specific DC's.
As an example...Climb has DC's listed as follows...
DC 0 Ladder
DC 10 Rope
DC 15 Uneven Surface (Cave Wall)
DC 20 Rough Surface (Brick Wall)
DC +5 Slippery Surface
DC +5 Unusually Smooth Surface
EDIT: Also these are player facing, being located in the PHB, so this isn't a case where majority of players won't see these... it's a case where the designers are very much letting players know what the expected color is for DC's in the game.
5e has plenty of this sort of thing too. The Basic PDF - mostly in the equipment list, which is clearly "player facing" - has DCs for extinguishing the flames from Alchemist's Fire; for moving over scattered ball bearings without following over; for moving safely through a field of caltrop; for breaking chain, a snare, rope, a net, or manacles; for avoiding a snare; for escaping from manacles; for picking various locks; for making a forced march; for surviving without water; for clearing a low obstacle with a jump; for landing on one's feet when jumping into difficult terrain; to avoid being dismounted; for stabilising a dying creature and recovering from injury and disease; for maintaing concentration on a spell; for escaping from rubble following an earthquake.
If it's a DC 10 DEX check to move at full speed through an area with scattered ball bearings, that seems to generate an expecgtation as to what (say) the DC to walk across a log without falling off (presumably no higher). If it's a DC 20 STR check to break a metal chain (!), then we know that there aren't very many doors about with a higher DC required to break them down. Etc.
This is why I don't see either 4e or 5e as a principally freeform system. But it's also why I don't see this asserted difference between them in this particular respect.
With my limited experience with 4e (and without referencing the few books I have), I would say that between the utility powers, etc. It was much clearer what kinds of actions were genre-expected in 4e (mediated by tier/level) than it is in 5e. A position boisterously espoused by other 4e supporters on this thread.
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I grant that there are other aspects of the two systems which factor into this perception of a loss of martial parity (particularly the expenditure of resources via AEDU powers.)
I'm reasonably familiar with 4e's matial utility powers. Rogues, for instance, get a number which allow them to hide without adequate cover or (at epic tier) with no cover required and no check required.
I'm not sure how this would be done in 5e - presumably by piling on DC numbers and/or imposing disadvantage on the check.
But I'm missing how this has any bearing on the issue of which is more freeform. Both systems have significant numbers of non-check-based, non-GM-mediated- "goal and approach", resolution sub-systems: powers in 4e; various class abilities including spells in 5e. These sub-systems set parameters for what is possible in the fiction. Eg the 3rd level 5e thief gets "Second story work", which is anaolgous to a 4e at-will utility power like Great Leap (2nd lvel) or Nimble Climb (6th level); the 2nd level 5e fighter can use Action Surge to boost his/her movement, which is somewhat analogous to the 4e 6th level skill power Mighty Sprint.
What's the DC, in 5e, for climbing at full speed when not a 3rd level thief? What's the DC, in 4e, for climbing at full speed when not using Nimble Climb? The approach to answering these questions is, as far as I can tell, fundamentally the same in both systems. It's not affected by the slightly different resource schema in the two systems (except to the extent that what the GM has to keep in mind is resource scheme X in 4e and resource scheme Y in 5e) and it's not affected by the different player-side resource pools, which (in 4e) don't factor into the setting of the DC but rather allow the player to affect the output of the roll (ie after the DC is set), or perhaps to reframe the fiction before declaring the action (ie beofre the GM needs to consider setting the DC).
part of the process of action resolution in 5e is that the DM can determine whether an action is possible or not
If we are talking about actions that are declared outside the context of a formal rules sub-system like a spell or class ability then, again, I don't see the contrast with 4e. 4e I think encourages a different
ethos when it comes to deciding what is possible, and in my view provids better support for translating fiction through action into consequences (via the skill challenge structure), but the actual
procedure of adjudiction for these action declarations I think is the same.
Now if the claim is that 5e is more freeform than 4e because it allows the GM to override (say) a class ability like Second Story Work or Action Surge, well that's a very different claim from what I've seen so far in this thread. Personally I don't think that
freeform, in the context of RPGing, is a synonym for
GM decides.