I recently recorded a violinist and cellist for a trio piece (with piano) I was working on. I don't work very often with real players (they don't come cheap), so I started by recording them separately, one at a time, like you would do with MIDI parts, because that's what I'm used to.
When the recording was done, the players – who know each other well and often play in large ensembles together – told me they could do much better if I recorded them together. Especially for my piece in which the piano was recorded with no click and with lots of rubato.
I'll just say that I was thrilled by listening to them play the two parts at the same time. Dynamics, intention, rythm, it was really something else. They really do play differently, and much better, when they have another part playing simultaneously next to them.
I ended up using the separate tracks because they were good enough and to be able to do some stereo separation and EQ (I'm talking really low-budget here...) but to me it proves DG's point.
Just my 2c.