Male here, so, no experience with the running skirts (as far as you know...) ;-)
But, as can be seen on my posts on the tri forum, I am fully invested this year in compression garments and, seeing no responses to your question about tops, I will throw in my 2 cents. The compression tops are not restrictive and do not feel "tight." They are not anywhere near as thick, tight, and supportive as a sports bra (from what I can tell having never worn a sports bra). They are not as thick as running tights and really do not feel like they are squeezing you, liking running tights sometimes feel. In fact, they really do not feel like they are "compressing" anything. Compression socks feel like they are compressing, but, the tops do not really feel like that.
The best way to describe it -- when you run, it is actually pretty brutal on your entire body. The impact shakes everything, including your upper body (torso, arms, back, etc.). Over time, those little ripple cause fatigue and soreness. The compression tops kinda "dampen" all those little ripples and keep you from getting as tired and sore as quickly. Hard to explain b/c the tops do not squeeze and hold everything in place, just kinda dampens everything. I like it b/c my lower back does not get quite as sore and my arms feel better after long runs. Plus, they are really, really light, and the white tops protect from sun and create a cooling effect when they retain water and have wind pass over them.
Is it really that incredible an experience? Meh. Not really. But, I have noticed some advantages of wearing the tops for long training runs. But, do not think you are going to be wearing a full-body support bra like top. Not like that at all.
P.S.: By the way, I am using the Skins long sleeve top (in white) and the Skins full tights (in black, cause white tights ... yeah ... not a good idea ...).
If there are no dogs in Heaven, then when I die I want to go where they went. - Will Rogers Emery's Third Coast Triathlon | Tri Wisconsin Triathlon Team | Push Endurance | GLWR