I've always felt limited by my lungs. They simply don't blow off enough CO2 and take in enough O2.

It's pretty much the limiting thing for many of the pros too.

I do try on a daily basis to take as deep a breath as I can and then expel as much as I can, slowly. If it makes you cough, then you definitely need to do them regularly. A handful of reps each day does wonders.

I've sometimes tried to see if deep breathing helps while riding for things like climbing at short high efforts. But I get mixed results. Problem usually, I think, is that for me real deep breaths happen at too slow a rate.