P-basses have a lot of low-mid emphasis (thus the deep sound). Jazz basses have a lot of growly high mids (at least most of the alder-bodied ones that I've played do). So, it depends on what kind of mids you'd like to accentuate.
My Spector 5er has lots of growly mids too, I think most Spectors do.
+1.
And IMO Roscoe, MusicMan, and Rickenbacker. My Alembic Europa has great mids too. I thought my Lull J-style w/Duncan single coils had strong mids. I've recently had the Duncans replaced with a set of Bartolini's, it now has big-time mids.

Plus, my amp has a decent eq, so I feel I can dial in decent mids from any bass that I use.