I think it depends on the look you want, and how much time you want to put into your decorating. I don't personally like to eat a cookie with fondant on it, but I do like glazed ones. Plus I like the look of the glazed ones, so that's what I do. If you're in a hurry, or if you like the taste of them with fondant on them, do that. You're really you're own best judge of what you like, and if in doubt, bake a batch of cookies and decorate them both ways to make up your mind. 
Plus you get to eat cookies that way.
Deanna
Deanna and I are completely opposite! I don't like glazed cookies and I don't like decorating with it. I do love eating fondant-covered cookies and I love decorating with it. There are certain designs that work better with each, but it's definitely just personal preference.
Correct me if I'm thinking wrong, but Fondant, Glaze, and Royal Icing I consider 3 different types of decorating. I prefer Toba's glaze as the base on my cookies and piping and detail work goes to Royal Icing.
I only tried fondant once, no one was crazy about it. I will admit fondant was easier to work with. I have'nt mastered the thinning, or thickness of Royal Icing yet. I do love the way it grabs coloring though.
I seen some people use just Toba's for base, piping and detail on the cookie and some use just Royal Icing for everything. I don't know where I came to put both on, but I get more compliments on taste for them. I'm sure it came somewhere on CC. Maybe it cuts down on the sweetness. I don't know.
Carleen
yes, they are 3 different types. That is my question - what each person prefers before decorating with RI. Fondant or glaze. I prefer the taste of fondant, less sweet. But the glazed are so pretty. And when I run out of fondant, I think "oh yuck! I have to make more fondant".
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