One thing I do know for sure is that it is expected that after colliding with Andromeda it will become an elliptical galaxy. I think the same is true, or at least believed to be true for most if not all spiral or spiral barred galaxies after enough collisions with similar sized/mass galaxies.
This leads me to believe that it has to do with the age of a galaxy, or more precisely how many merges it has had in it's life time. I am not certain of this part but it is my educated guess based upon this that most if not all galaxies start off as spiral galaxies and ours is just younger in that regard. I wouldn't post a response with a guess normally but I did give factual information as well, and am just giving my guess to continue the chain of logic. I'm going to research that now though. As for the barred aspect, I haven't a clue.