Just wanted to chuck my opinion into the fray.
I did some recording a few months back, first time recording with my current band and we were recording a 4 track EP. We never expected the best quality recordings but the quality is still pretty damn awesome. I took my Ampeg with me so I could get the sound I like, but the producers equipment didn't seem to react well when we DI'd the Ampeg. The guy didn't have a bass cabinet so we couldn't mic it up, he just put me through a Sansamp BDDI.
Now I wasn't really happy about the new setup, but it was time saving and I ended up being able to dial in a half decent tone. I was happy with the recordings until we got the mixed versions back and I realised that my bass actually sounded incredibly thin compared to usual, and that alot of sections in the EP sound very empty.
In the end, it's all about the time you have and doing what's best for the band. If you are paying for the sessions, you need to be able to be ready to record as soon as possible, otherwise it's money going down the drain. That's why I'm always happy to DI my amp, as I get the sound I like and it takes maximum of a few minutes to get everything sorted out.
Just my opinion.