It should also be noted that in chase scenes, "warp 5" is a universal measure of speed: our heroes and villains can both declare "we are traveling at warp 5", which then means that neither is gaining or falling back. The speed a certain warp factor corresponds to is not dependent on the ship, its engines, or its history of acceleration, then.
In contrast, there is no such universality about the command "full impulse" or "1/4 impulse" in the dialogue of any episode or movie. One ship's full impulse may well be insufficient in catching up with another ship's one-quarter. And the engines may be set at 1/4 impulse and still only move the ship at crawling speed initially, as we see several times when Kirk's ship leaves the spacedock in the TOS movies.
Nor is there any indication that the speeds reached by impulse engines would really be limited to 0.25 c. This is just a Starfleet recommendation that is mentioned in the Tech Manual, not something that would limit all heroes and villains on screen. For all we know, our heroes regularly do something like 0.75 c at impulse. That is, after they have accelerated to that speed, which may take hours or days of running at full impulse.