Steyr has contracted with Sabre to make US AUG A3. They use as many Steyr parts as allowed by 922r. That said...
A3 =
Pros: uses AUG parts (maybe a plus?), has a longer rail, clean.
Cons: uses AUG mags only but you buy a NATO stock, then there's no left hand option, 1:9 twist 16" barrel only, no traditional optic option, expensive, teething issues (recall)
MSAR =
Pros: there are some improved parts - bolt sleeve is milled, larger thrust piece, etc., more modular, more accessories, E4 option allows use of AR mags, left handed option available on both stocks, 1:8 twist barrel available in 14.5", 16", 18" bull and 20", there's bunches out there, parts are all US made and available, customer service has been tops, STG-556 prices are in AR territory and E4s are ~$400 more, there are traditional styled optics available though discontinued, supposed to be kits available in 5.45, 6.8 and 7.62.
Cons: E4 is too cluttered with extra rail attachment points IMO, David is gone so customer service might be a question, there were some teething issues, MSAR can't keep up with demand and some E4s are lacking their options (like 1/2x28 threads instead of 13x1L), 5.45, 6.8 and 7.62 kits are still MIA
I have an E4 and it has been fine with P-mags, factory mags (amber XM-17) bind up and there's supposedly a follower redesign in the works. I just sent my stock in for a mag catch replacement, it works but sticks a little with USGI mags, after speaking with Paul @ MSAR about the mags binding. He basically said to send it in even though mags are working b/c eventually they'll stick and not come out; there's a stainless replacement available so why not?