I' ve hunted Fallow many times.
Maybe the biggest difference I' ve observed compared to most other deer species, is that:
1/. They like to live/feed on the edge of the bush, and will wander out to feed in the open on dusk/night. Often still there in early morning.
2/. They are territorial and tend to stick to a set area and not wander far. Often they' ll return to the same place after they have been disturbed.

Otherwise most usual deer hunting techniques are effective.
I haven' t hunted them in the rut, but beleive they are quite aggressive and vocal.

Hope this is helpful.