I'm with Cougie on this. I've been running in compression tops for about 3 months now, and to be honest, i have not notice any benefit with regard to my breathing.
I never bought the top(Skinz a400)for that purpose anyway, but more because someone told me that compression tops were great for stopping nipple chafing. and they have absolutely done that for me, not a single chaf for the past 3 months, and I've been doing anything up to about 24 miles in it.
Slightly of the point, but hope that helps.