To suggest that any archer is better than another simply because of the bow he uses is flawed.The English archers,as i'm sure the Eastern archers were,were highly skilled and usually trained from a young age due to it being a popular sport in certain counties in Wales and Southern England.Englands tactics at this time revolved around a mass of arrow fire into enemy formations but that does not mean they were any less skilled individually should the need arise.
I'm not trying to say anyone is better than another as a skilled archer is a skilled archer no matter what bow he uses but the simple fact is the Longbowmen of England had a massive impact on the medieval battlefield during the period of the 100 years war and i feel this should be reflected in the game.
This dosent mean they have to be uber but their quality along with unit and game balance should be taken into account.