Something about Bows:

1.- There's no such thing as a mounted longbow, you could never shoot a longbow from horseback, the only closest thing to a mounted longbow is the japanese asimetric yumi, so the MTLG is a composite Bow, not a longbow

2.- No Bow in the entire medieval world gets even near in effective range to the welsh/english longbow (200 yds.), since longbows were as tall as their wielders, and required a long training for a man just to draw their full lenght (some LB's were calculated to have a pressure of 95 lbs!) Again, the only second place is for the yumi (160 yds.) (these japanese people really did good bows!) the other difference was that as puzz3D stated, longbow arrows were longer, heavier and used the (in)famous bodkin tip (ask the french chevaliers!) the japanese yumi used arrows even longer than LB's but they were thinner and lighter and had really big feathers in the tail so the japanese arrows sort of "Flied" more compensating the less pressure of the yumi, but had less armour penetration.

3.- Composite Bows didn't have too much more range (140 yds.) than a short bow (120 yds.) indeed, some composite bows are really small even compared to a western shortbow, the fact is that they were just more powerful (that gives the extra range) because of their strong and very flexible construction (incorporating animal bones and nerves) they lost little effectiveness at long range compared to sbows.

So, you can give the shortbow to all western (and some arab) (not turks) units (including western horse archers)
(range- 5500, velocity- 175, accuracy- 0.7, lethality- 0.7, power- 1, armour mod- 1 reload time- 5)

the mtlg to the turkish (and some arab and eastern european) foot and mounted units.
(range- 5750, velocity- 190, accuracy- 0.75, lethality- 0.7, power- 1, armour mod- 0.8 reload time- 4)

and the ninj (mongol composite bow) obviously to the mongols, cumans and volga bulgars
(range- 5850, velocity- 195, accuracy- 0.8, lethality- 0.75, power- 1.5, armour mod- 0.6 reload time- 4)

and leave the longbow for the british (and maybe you can add some french longbowmen too) yes, french had a little quantity of longbowmen from brittany and normandy...
(range- 7000, velocity- 200, accuracy- 0.75, lethality- 0.9, power- 2, armour mod- 0.5 reload time- 5)

cheers,

Tyberius.