Ghee, for those of you who don't know, is essentially clarified butter. That is to say, we have "clarified" the butter - or, removed the parts that make it look cloudy. To make clarified butter, you slowly heat it until all the milk proteins have separated themselves from the fatty goodness. You then strain the results using something like cheese cloth, discard the milk proteins, and use the clarified butter as you would use regular butter.
Ghee takes things one step further. You continue to heat the butter until the milk proteins turn brown. This gives a slightly richer flavor to the results, and also removes nearly all the moisture. Less moisture means it stays fresh for longer. Ghee is the sure winner.
But why not just use butter, you might ask? Some people, those who can tolerate dairy, do just that and include it in their paleo diet. If this is you, be sure you buy full-fat, high-quality butter to really get the most out of it. Most paleo enthousiasts swear by Kerrygold butter - either for using as-is, or for making their own ghee. This is because Kerrygold is advertised as coming from grassfed cows.
Basically, it's important that the cow be grassfed because what the cow eats ends up in what the cow produces (and therefore it becomes what you eat as well). I agree with this for people who eat the butter as-is, but I honestly don't think it's as important for those intending to make ghee. Most (if not all) the good-for-you nutrients are in the milk proteins... that you just cooked and strained out of your fat. Here you can compare the nutrition data for butter and clarified butter.
And to top things off, Kerrygold may in fact not even be 100% grassfed! Gasp, I know.
So, to finish off, my personal preference for butter is a local butter. Cows here in Belgium are all "grassfed", though nearly all are grain-supplemented for at least part of the year (there's not much grass during the winter months). I buy salted butter for the hubster and unsalted for my ghee-making purposes. I am not one of those people who tolerate dairy products, and even the tiny amount of milk proteins present in butter turns my intestinal track into a whirlwind of debilitating cramps. Fun, I know.
I feel so great avoiding dairy though, that I don't even want to eat it anymore. But butter is a fairly cheap fat, and it imparts such a lovely flavor to foods that I truly enjoy cooking with it. (PS - Clarified butter and ghee have higher smoke points than butter which means they're safer for cooking at higher temperatures! Win!) And besides, ghee is so easy to make!