I don't think that "better" or "worse" is the right metric here. When playing Cthulhu Dark, for instance, we know in advance that the PCs' lives will probably get worse (they will have horrible experiences and lose their grip on sanity). But that doesn't stop the players exercising agency in Cthulhu Dark play.
What is key is
do the actions the players declare, and the resolution of those actions, actually matter? Because
what matters is highly context-sensitive, so is player agency.
For instance, in your example, what is at stake in the players' successful recruitment (via their PCs) of the eagles as a player-side resource? If the goal is to avoid encounters, then the GM who allows the players to believe that they have succeeded, and then springs the orc encounter on them anyway, is negating or disregarding player agency. If the goal is to avoid the exhaustion of travel, then the GM who springs the orc encounter is probably not negating agency: the players get the benefit (be that mechanical, or fictional positioning, depending on system) of confronting the orcs unexhausted.
This illustrates why a useful tool for helping to preserve or enhance player agency is to understand what the players hope they will achieve on a successful check. Eg if it is clear to everyone at the table that the goal of the eagle gambit is to avoid encounters, and the players succeed on the relevant check(s), then it will be crystal-clear what the GM is doing when s/he nevertheless springs the orc encounter. (I think this relates to
@Ovinomancer's comments upthread about techniques that avoid illusionism.)