When you apply for a mortgage, lenders pull your credit report from all three major bureaus — Equifax, Experian, and TransUnion. They use a specialized version of the FICO score (FICO 2, 4, and 5 for mortgages) and typically take the middle score of the three.
If you and a co-borrower are applying together, the lender uses the lower of your two middle scores. That means improving the lower score often has the biggest impact on the rate you'll be offered.