Do you like Chevy's or Fords?
Just Kidding....
I have a JL T-45 Hawk, it is slightly smaller than the FB Hawk, the FB Hawk has more scale Detail (rivets etc.) however I don't believe they offer the T-45 version, as your question states BAE Hawk I guess this would be a non issue.

As far as building, they ALL take some tinkering so I would say it is awash, just look at the many building threads on both products.

I think the real issue here is availability, as far as I am aware it is very hard to get a JL T-45 at the moment, they are very much in demand, not sure of the status of the FB hawk.