Surgery bras or compression bras generally are latex free, generate a lot of compression, and have adjustable shoulder straps and back straps. The adjustability is very important, because as your swelling goes down with time, your surgical bra can accomodate the slight shrinkage of your breasts over the first couple of weeks after surgery.
Sports bras generate OK to very good compression. However, not all of them are latex free, so may cause a skin rash if you wear them for long periods of time. They often do not have any adjustable shoulder straps or back straps, so as your swelling goes down, it may become a little loose. One strategy is to buy a sports bra that fits right after surgery, with the knowledge that you may have to buy a better fitting sports bra several weeks after your procedure.
In the end, the choice is yours, but most plastic surgeons will consider a sports bra part of the procedure. This way, you know you will get a garment that fits you after your breast augmentation.
Best Wishes,
Roy