Either one will definitely work for nursing -- assuming we're talking mei tai to mei tai here (the Oh Snap with buckles is a buckle carrier, not a mei tai, and very different).
The Kozy is a taller and wider MT than the BabyHawk, and the straps are at a wider angle. I tend to find that if you have very narrow shoulders, the BabyHawk will work better.
The BabyHawk has a very firm headrest that can turn down or be up supporting baby's head. Kozy has good head support with a little extra cushioning, but it's not as stiff.
Kozy is better for high back carries with newborns/small babies because it's so tall. The ToddlerHawk works well for this but not so much the BabyHawk IME.