Its a little bit connotative and a little bit definition for those of us who were whipped in the STEM paper mines for all those years.
Alas is grief pity or concern, while unfortunate has the first definition of unlucky and second of unsuitable.
So the statement "Alas, the results did not support this analysis" implies that I personally wanted a particular result, which I shouldn't when mining papers, and it sounds a little dramatic anyway.
The statement "Unfortunately, the results did not support this analysis" implies that the results were just unsuitable/bad luck for the analysis, and although its a little odd to call up bad luck, basically you're shrugging your shoulders and saying it didn't work rather than grieving the results.