| The Fulltone Bass-Drive in my experience (and I've owned three of them, all different versions) loses a good deal of lows in the FM and Vintage modes. The only mode I could get away with using it in in a band mix without my bottom dropping out when I kicked the pedal on was the Comp Cut mode, which, when run at 9 volts and with the addition of the boost switch, is capable of a decent amount of gain.
But that won't get you nearly as much gain as using an OCD, which is capable of a lot of gain depending on the output of your bass. The OCD will lose lows if you roll the gain off in my experience (at least that's what happens with my Version 4 OCD), but the bottom is retained quite well with the gain maxed. To vary the amount of gain with the OCD, I liked using a volume pedal in front of it (leaving the drive on the OCD maxed) or just rolling down the volume on my guitar. You can get a whole myriad of tones this way, with pretty decent bottom end retention. It can be very meaty yet always quite well defined on bass, especially if you run it at 18 volts (which I do).
If you want a wide array of sounds and levels of gain with decent bottom end retention, I'd have to recommend the OCD over the Bass-Drive based on my experience. If you just want low to low/moderate levels of gain, the Bass-Drive in Comp Cut mode run at 9 volts is quite nice. The Bass-Drive can be quite flexible if you don't mind the low end loss in the other two modes, but otherwise I'd say the OCD is actually more flexible if you use a volume pedal with it. | 
