I think you can do both, I used to do yoga and I now do Pilates. I don't think the breathing is all that different TBH.
I swapped to PIlates as I got fed up with all the 'be mindful, connect with the earth through the breath, love and respect yourself' waffle that seems to come with the yoga. With PIlates, you get straight down to the exercises without all the lectures and timewasting. So a 30 minute PIlates workout is 30 minutes of exercising, whereas with yoga (even the lovely Adrienne) it's 20 minutes of exercising and 10 minutes waffling.