Just did a test on custom battle; in a footrace on grassy plain, the trebizond archers are slightly faster, however surprisingly they also tire slightly faster than the guard. For me stamina is more important than speed, since in my experience horse archers tend to scurry away from foot archers before they can get more than a couple of volleys away, aiming to tire them out chasing them.

However, my conclusion is that despite their advantages guard archers probably aren't worth spending the extra money on upgrading to an archery range. For those factions where the only other option is peasant archers it's clearly another matter.