You do have a point that Infernape's versatility and Speed and the horrid side effect of Mienshao's signature move makes Infernape appealing, but still there's no denying that being able to recover off LO recoils is a huge boon. Also, the HJK behind the Attack from Mienshao is really good - it has no problems scoring a 2HKO on Skarmory after SR damage.
Seriously, Mienshao has a sufficient movepool to get stuff done. HJK + Stone Edge is enough power as it is, and it has Grass Knot, HP Ice, and very usable Special Attack stat to OHKO / 2HKO the likes of Gliscor, Slowbro, Hippowdon, Tangrowth, Jellicent with moderate investment in Special Atk (I went with 96 Atk EVs). It can set up a Substitute to ease predictions, and it can easily recover its health back with Regenerator. It can even function as a Baton Passer, passing SDs / Substitute.
I guess it's natural to compare Infernape and Mienshao, since they are both common scouters. I believe they each have enough distinctions to set themselves apart from one another - neither one overshadows the other.