Choosing between lenders

[Tyriq Royal]

Hello,

I’m between lenders and they both sent me back my appraisal. 
Lender one: fully approved & rate locked in.

Lender two: Conditionally approved and my rate is locked.

Lender two’s appraisal is 5k less than lender one’s but is offering 10k in equity for a first time homebuyer. Lender one is not. How much should the appraisal influence my decision in which lender to choose from assuming rates are the same?