My TSO has worked flawlessly with everything I have tried in it so far. Granted, I haven't tried that many brands, but so far it has handled all of them without a single problem.
I don't shoot anything but brass cased ammo, no steel, no aluminum, no reloads. I don't buy the cheapest, but then I don't splurge and buy the most expensive either. The majority of my shooting so far has been mostly just target shooting or plinking.....no competition.
The brands I've tried so far have been Winchester NATO 124 Gr, S&B 115 and 124 Gr, Winchester White Box 115 Gr, and Federal American Eagle 115 and 124 Gr. The TSO handled them all perfectly and from what I've seen shows no particular preference for any one brand. It shoots them all.