TIming, pricing, location, patience, experience.
These all play a part in how easy/difficult it would be.
SHORT SALE: Typically, it can take 45 days from the time an offer is accepted by the seller, before a loss mitigator responds to the contract. The short sale lender can accept, reject, or counter. HOWEVER....if the process was already in place by the time you submitted an offer, or if it was previously in contract but the buyer backed out for one reason or another, the bulk of the work is done. So if you submit an offer and it's within the parameters of what the short sale lender says they will need to net after the sale, your chances are multiplied.
Two of my short sale listings sold quickly --- in less than 30 days ---- to the second buyers who submitted offers after the first buyers backed out. The buyers and their agents were ecstatic. I was able to provide the agents guidance on how much they can write (oops, too low....) to make their offers stronger.
If the REO agent priced a listing low
If buyers' agents know it
if the property is in a favorable loaction, and
if the buyer's agent is informed about the market conditions
...you should have adequate guidance on how to write an offer.
Try to be reasonable and try to write an offer close to fair market value. By doing so, your chances increase.
Don't assume that just because a property is an REO, that you can write an offer for 50% below! Not all REO properties are priced correctly. Some REO agents deliberately price it low to stoke interest and induce multiple offers.
Your best bet: find a realtor who understands and knows how to do a short sale and an REO. You'll be better off in the long run.