Charlie Craven has an excellent article in this issue of Fly Fisherman about thread. He concludes pretty much what you’ll find from a little tying: threads are very different–some flat, some round, some heavy, some not. He also demonstrates why neither the “aught” system 3/0, 6/0, 8/0, etc. nor the denier measurement (which is the weight in grams of 9,000 meters of the thread) really help tiers pick a thread.
In case Charlie’s article wasn’t enough for you, here’s a table that covers details on many different threads: http://globalflyfisher.com/tie-better/fly-tying-thread-table