There is a good answer to a similar question, here
What to look for when choosing a dutch oven?
but since I had already written my answer, I'll leave it.
It depends on why you are buying it. There are several factors that go into picking any Dutch oven.
Weight/thermal mass. The ability of the oven to retain, and release heat evenly is determined by its thermal mass, which is why they are made of cast iron and very heavy. Cooking quality for both with be comparable. Both are VERY heavy. There are other brands that work...there is a Mario Batali Dutch oven that has gotten good reviews, and I even have a Tramontina that I bought in a grocery store that is very well made and works well.
Lid fit. The lid has to be a good fit. If it is loose, or warped, when you are doing a braise the liquid will escape and your braise becomes a dehydrate or a burn. This is where "cheap" brands fail. However, either of these brands will do you well.
Thickness/evenness of the finish. This is, in my opinion, more aesthetic and long term care based, but if you are going to buy enameled, make sure you get a decent finish. There are some that look more like the enamel has been painted on. This is mostly your call. The problem with enamel finishes is that you have the chance of cracking or chipping it, and once that's done, there is no cost effective way to fix it. But the enamel affects the cooking least of all. I cook most things in my Lodge cast iron (no enamel) dutch oven, and while it affects the color of some dishes, there is the additional iron that I get in my diet...no Geritol ™ for me.
Cost. You can compare cost, but this will potentially be the biggest variable. It's why I own the Tramontina.
Status. This is a non-factor for me, but if you take dishes to your gated community potluck, the Le Creuset has more status. It is, after all, French.
Both are good brands, both will allow/help you to cook good food. You have to determine what the cost/status difference is between them, and how important that is. If both cost the same, I would probably go with the Le Creuset. Since they rarely do, I have more Lodge than Le Creuset in my kitchen.