Reviews online generally not favorable for the Tiburon Bag Check ... Complaints of "Expensive per-hour fees", staff that is sometimes not available at pick-up time, and mishandling of baggage (throwing bags around).
I'm not terribly concerned about their prices, but I'd be highly annoyed if no one was there when I needed to pick up my bags, and I don't really want my bags thrown around either.
Besides, if ClubAcela will do this, it's one less chore to run.
Note: I've never actually been to this station, so I'm basing my opinion entirely on other people's reviews online...