Do lenders tend to favor one of the CRAs, do they split inquiries between the three or does it just depend on the bank?
That entirely depends on the lender.
General rules of thumb:
Big honking, national banks: pull any of the three primary on at least two factors anecdotally:
- Where you live. Note, if you've only lived for a small period of time (couple of years) they may pull on your previous address too.
- If they already have a relationship with you, they may pull a different bureau just to increase their resolution of you as a customer.
Smaller banks / CU's, or some international banks, often only establish a relationship with one of the bureaus and pull them almost exclusively.
There are some strange corner cases too: many lenders will pull additional bureaus in the event of a marginal approval. Also, some strange outliers such as Care Credit is traditionally EQ, but almost everything else underwritten by the same lender is TU, though I think this may have changed recently. These things are very mutable unfortunately, and these days the three CRA's are in direct competition with one another after the old regional affiliation model broke down.
In any event, your best bet are to check the various credit pull databases, and just see who does what specifically and try to figure it out from there from recent entries.