Gee, I could usually tell within a couple of bars which composer it was. The orchestrations and rhythms that McCarthy, Chattaway, and Bell used were very distinctive. Bell was particularly easy since he routinely did his Trek scores in waltz time. I think he also used more French horns than the others. McCarthy was big on brass and strings and used pretty steady 4/4 time. Chattaway also used a lot of brass, but less solo trumpet, and less cello and bass than McCarthy; he also tended to make more use of long sustained notes and varying or syncopated rhythms, without the same kind of driving ostinati that the other two used.
A few bars usually gave the composer away for me as well. Bell was especially easy because there's a particular harmonic progression that he beats into the ground. Chattaway's orchestrations are leaner than the other two, with more usage of solo instrumentation. McCarthy is just a big wall of sound.
In Enterprise, it got increasingly harder to identify the composer partly because their usual patterns were broken but also because there were more of them.