"Would it be significantly wiser to use the full spelling or does it not really matter because you are ranking for keywords with anchor text?"
Well it really depends on if people search for the acronym and if the acronym is your primary KW target. In the case of
SEO they do and it probably has as many or more searches than it does spelled out. OPM (Outsourced Affiliate Program Manager) wouldn't be as good because many people don't know the acronym and everyone is going to search for all the words.
In general the shorter domain the better for branding - search engines don't mind if it's pretty long. In general the more targeted the domain the better it is for Adwords. A human review would consider the acro if it's well known - not sure if the algo takes it into account though.