For teaching, I've been using overheads, and have been since I started. Even as a TA I used them now and again. They're flexible and don't require a great deal of planning ahead. Five minutes before class, if the photocopy machine is working, I can run off more overheads. They're easy to make.
Today, for the first time, I taught with slides. I put together the carousel last night, ran through the images, everything worked fine. It was in good working order for today's class. Today was a different story. Everything worked - except for the light bulb which makes slides visible on the screen. Not having a backup plan - and not being able to give the lecture properly without all the images about which I'd intended to speak - I was able to locate my advisor, who generously came to my rescue. It wasn't just me. The bulb was out and the spare bulb in the case turned out to be the wrong kind of bulb. I borrowed a key and fetched the other slide project which - thank goodness - functioned, give or take a malfunctioning reverse button. I gave the talk "only" twenty minutes late.
I like slides, but projectors just weren't made to be lugged around. They're relatively delicate, with multiple movable parts compred to overhead projectors. The image quality is much better, true, but making slides requires planning well ahead. They're a good long term investment. (Or would be if Kodak hadn't recently announced that they will no longer be making slide projectors.) I might be willing to teach with slides if I had a classroom with a dedicated, mounted projector or two and backup parts and pieces. I might be willing to teach with slides if I had the time and planning to assemble a relevant collection. For now, however, I'm sticking with overheads.