I use and have been using Uni 8/0 for years for my tying and have had no problems. I have my beginner fly tying students use Uni 6/0 because it is not as easily broken with tying pressure that beginners usually apply. I have noticed that my students will have a breaking problem due to the way they are doing the whip finish. I instruct them that the whip finish must begin at the very front of the thorax area of the fly and wind it forward to the back of the hook eye and then remove the whip finisher and snug up the whip finish. I find that those that break the thread while doing the whip finish have started their whip finish behind the hook eye and wind it to the thorax area. This causes the thread to bind against its self and will break or bind up at times. I have also noticed that they will sometimes do their whip finish all in one place instead of winding it forward and this will cause the binding and breaking problem for them. Another area I have noticed is that some hooks have a rough place at the hook eye where the hook shank meets the curved hook eye and that rough spot can sometimes cause a breakage when you are snugging up the whip finish. I am not saying that you are not doing the whip finish correctly. I am just saying I use Uni and have no problems and stating the problems that my students sometimes have. I cannot report on the Uni 3/0 because I have never used it.
Warren
Fly fishing and fly tying are two things that I do, and when I am doing them, they are the only 2 things I think about. They clear my mind.