Many designs can be done in either buttercream or fondant.  Both applications can be smooth, but have different looks.   Fondant is a sugar dough that entirely covers a buttercream cake.  So it is another layer and therefore the reason most cake designers charge more for fondant.   There are some designs that really do need to be completed in fondant such as the topsy turvy styles, stenciling, detailed appliques, and styles that look like fabric.    

Also a fondant cake is best in outdoor wedddings due to heat, exposure, etc.   You might also want to consider fondant when choosing vibrant colors on your wedding cake.   Red and black can make nasty stains in the teeth and mouth for your guests.

Sometimes it is a matter of preference of the decorator.  Some cake designers are more comfortable working in buttercream and some in fondant.   Ask your designer which method they prefer to use.