I voted free standing because we have a door bouncer and sam LOVES it, but he does throw himself at the door frames and pulls off any sort of padding I try to put up now! (Was perfect until he got a bit bigger though)
We've just got a Fisher Price Rainforest Jumperoo (I started a thread on here about it if you are thinking of getting a free standing one) and Sam really would stay in it all day if he could - he absolutely loves it, and there's so much for him to play with on there too when he's not bouncing! More expensive but worth it! x