I think it depends on how you set up the session. You can get a sound and track all the basics with the same set up, or choose to follow the song's needs and change up the signal path for each tune (or even each section of a tune).What i've noticed is that modern CDs sound more and more like several records that were juxtaposed onto the same CD track. The colors and textures are so different from each other. The older recordings are, the more they sound like they were coming from the same pot. Now there's more separation but less credibility as a live recording.
One method may give an album a cohesive feel, while the other may be better for each song individually.
Although there are albums that use very different signal paths song to song, and yet as a whole the album works.
I like albums in both of these styles. If it sounds good I don't mind hearing the same sound for the whole album, then again it is cool when each song sits in its own space and time.
For whatever that is worth