It has only been briefly mentioned, but an all cash buyer usually means a quick closing meaning the seller gets paid soon. With a financed deal, usually (at least frequently), the prospective buyer may have to sell or close on another property before being able to close on the sellers property. If they have trouble selling their property, or their contingent sale doesn't go through, it could significantly delay the closing of the sellers property.
There is also one financing situation that has not been discussed. That is, where the buyer is using a "line of credit" to purchase the property. In that case, the buyer offers another property (or other asset) as collateral to a bank and gets a line of credit.
In this case, the loan is not secured by the property that's for sale, it's secured by the other asset. The new buyer doesn't need to have the bank approve the purchase of the new property and (generally) the bank doesn't know or care what they're buying with the money.
In this case, a (savvy) seller would probably consider an offer with this sort of financing to be as good as a cash offer. It would then be a matter of the seller considering any contingencies of the offers.