Through the deep woods, sure I'll agree. Over rough terrain like mountains or rivers? Again, sure. But over open terrain there should be no reason that a group of 100 soldiers on mounts...even with a baggage train...shouldn't be able to run down a group of 15 soldiers on foot. Especially over an extended chase of several days. No soldier can keep moving at that speed without rest or sleep, no matter how elite they are. You can push horses much further than you can humans. So adding a fatigue modifier makes sense.
You'd still be able to have an escape mechanic. Wait for the large party to be near a forest to make a break for it. Or take that rough trip over the mountain pass. It should be easy enough to 1) adjust the terrain modifier to impact different parties differently and 2) keep track of how long parties have been moving and simulate fatigue on both mounts and soldiers.