a bank loan will give you a bit more negotiating power.
Also, not true for everyone, but my credit union offers 1.9% financing on used vehicles. no used car lot will touch that.
Maybe not a rock lot, but a real dealership can do that all day long for qualified buyers.
And to be honest it does not give you any leverage at all in negotiating.
Dealerships get a small kickback for any loan they send to a bank, so if you finance elsewhere it cost the dealership money in the form of a kickback they'd get from the bank.