Definitely take the DI from the pick up. You can always choose to use it or lose it in the mix. Having said that whenever I mic and DI simultaneously I place the mic closer to the fingerboard to pick up the fingernoises that the DI lacks. Blending in the fingernoises gives a little personality to the muffled/stale DI sound. 9 out of 10 times I use both, and blend to taste, adjusting for phase coherence.
I like to use a large diaphram condenser on something like an upright bass. My goal is usually to pick up the higher end detail with the condenser since most pickups will pick up a lot of the bottom(or mud).
Hope that helps!