How much impact does an all cash offer have on an REO?

[Matt Gee]

I know this doesn't have a succinct answer, so I'd love to hear you anecdotes.  

I have heard only generalized stories, saying that basically all cash is better, you can get it for less, less garbage for the banks to deal with, fewer potential issues, etc.  

Say a home is listed for 50k, how much more play would you feel you had going in cash, does it really matter?