Slide projectors do matter to a certain extent. Some are more prone to slide jamming than others. All of them has a "default" lens that's usually crappy. Some (like the Leicas and Kodaks) can let you replace the lens, other's don't. Then there's the AF mechanism, which tries to focus every slide. On the cheaper projectors this can be cranky. Power is another issue, the more powerful ones can project from a larger distance. But the common one is 150W.
Related issue is the tray type. Kodak Carousels use a round (carousel) tray. Straight-tray types uses various straight trays (standard, CS and LKM) which holds from 40 (std) -100 (lkm) slides iirc.