I have tried several times to catch him. I am not able to or am I missing something?
I literally just completed that part. I tried one time and he got away, so I just used a couple of throwing knives the second time.
I'm-a Luigi, numba the one.
I managed to catch everyone who flees in those Assassin's Temples first try, try air assassinations.
Because I said so.
I think it's almost impossible to catch them before the last stretch of ground (without using throwing knives). At least I thought it was scripted like that, otherwise it's too short and the collapsing of rocks happens without a chase... Anyway, I always managed to jump on them at the very last part of the chase, which is all straight: the path divides in two; the templar goes one way (the flat way) and the other way is a small rising part parallel to the templar's path. On here you can sprint and jump on him as you are close to him (the jump propels you forward a lot too so you don't have to exactly be beside him).
I've never been able to catch him. :(\
Does it really make a difference though?
If you catch him, the guards won't be alerted and the room will be easier to get through. Otherwise you have to fight them; but even then it's still easy to dispatch them.