As you can see, there are many variables, as the realtors from way other unrelated market areas have pointed out.
However, what I've seen in the same zip code as your question originates from as well as other zip codes nearby, and being that all reo offers in our area must be accompanied by either a proof of funds or pre-approval, then the highest offer typically wins the bid.
I've not seen reo reps make a distinction that a cash offer is better than a financed offer.
However, they DO typically give preference for an owner occupant's bid over an investor and most reo's from HUD and Fannie Mae have a couple weeks where they will not even consider an investor bid at all.
Now, speaking of HUD, I think their new system is still a little crazy. I have submitted bids for an investor (after the bidding had been opened up to investors and was on "daily bid closings". My buyer's bids were above the asking price and HUD simply cancelled his bid!
This makes no sense to me, because this is like a reserve auction and in a reserve auction when someone has made the high bid before the close of bidding and has met the reserve price (in this case the list price) theywin the bid!
Not so with a HUD home. Other HUD buyers have expressed their same confusion with the system, where they made bids higher than the asking price, and got turned down, but later saw that somone else bought the property for less money! I think something is still broken with that system, but it is what it is.
I'd be happ to help you in the future with your homes, and am willing to bet I would be better help than soeone from say, Chicago or California or Florida who each have compeltely different laws than we do here.