Cash talks, as the old saying goes. Financing is subject to so many variables that if I was presented two offers on a listing, one full price cash and the other slightly more but financed, it would be hard to turn down the cash.
The variables that would make me consider the financed offer would be a large down payment for the financing with a strong pre-approval letter from a lender I trusted. Substantial earnest money along with the financed offer would also weigh in its favor.
Ultimately, it would be my seller's choice. If the non-financial aspects were more favorable they could also tip the scales, such as closing date, selection of my Title & Escrow versus others I'm not familiar with.
If you are the buyer, offer cash and the opportunity for a quick closing or a delayed one if the seller prefers it.