For perfect examples of the differences between cream and powder blushes, just take a look at Nars Cream Blush versus Nars Powder Blush. Cream blush is generally more pigmented, making it great for deeper skin tones, but also more hydrating, so people with dry skin benefit from it as well. Powder blush, on the other hand, is more transparent and better suited to oily skin, since it won't slide off the way cream does.
If you have oily, deeper-toned skin or fair, dry skin, there are exceptions to the rule, though. A staining blush like The Balm Instain Staining Powder Blush will last longer on oily skin, and a sheer, buildable cream blush like Yves Saint Laurent Creme de Blush is great for dry, pale skin.