I think it depends more on the quality of the blog, domain age, links pointing to it, etc. If its a wordpress or blogspot blog that was obviously put up a week ago just to make one blogpost for a link then it will have little or no authority. However there are some great, high ranking blogs from blogspot and wordpress that have been around a long time, and a link in a guest post from those would help quite a bit. I would say it matters more how trustworthy the site is, not so much where its hosted.
Having said that, if two sites had the same ranking factors, same domain age, same links, etc. and one was hosted privately and the other on wordpress, I would think they would give the edge to the privately hosted one. I would think otherwise it wouldn't have much of an effect at all.