I have played other mods with movement adjustments, but EB seems to have achieved a sweet-spot in my opinion.

Fresh troops move at a reasonable rate, but light troops can rings around heavies, and cavalry are fast enough to achieve tactical surprise (in other words you have to anticipate cavalry flanking if you want any chance of intercepting with infantry).

Exhausted troops become dramatically slower. This adds a whole new tactical challenge over Vanilla, because you have to try to rest troops before they become exhausted.

Recovery from exhaustion is fast enough for you to contemplate using the troops again before the end of the battle, but slow enough to compromise any blitzing plans you may have had.

All in all, I think the current movement and exhaustion/recovery rates work very well. Of course I have experienced the frustration of exhausted heavy infantry running so slowly they leave a slime trail - but at least I know it was my own fault.

The only problem I have with all this is that auto-resolve is unbalanced, forcing me to play almost every battle. However, this is not the fault of the EB team as I believe RTW is hard-coded to use campaign difficulty for auto-resolve.