In HPMOR, it also penetrates at least some thickness of cover, according to Moody, who also suggests that it does need significant mana. (How much mana? I'm getting the impression that Stupify is acceptable for Auror-level combat despite being castable by top first-years.)

It also cannot be countered. We don't see much of countering in HPMOR, but we do see Susan try to counter an extremely powerful bully's spell in the SPHEW.