Having done both, I prefer Great Lakes Crossing to Birch Run. I like the fact it is inside and you don't need to move your car from lot to lot. Many of the stores are at both locations. Great Lakes Crossing also has better restaurants and entertainment options as well.
I would just do Great Lakes Crossing. As another poster said, it's about 40 miles closer than Birch Run, indoors, and offers a lot of the same stores. Also, there's more dining options around GLC than BR.
To add, if you're staying in Detroit, avoid the outlet mall in Howell. I-96 is closed between Telegraph and Newburgh and will make your commute a complete nightmare.
Both are a long hike from Greektown and unless you're looking for something very specific aren't worth the trip. Most of the experts agree that they once were a place to find great bargains, but now are just ordinary malls. You would do better off at Somerset and the Oakland Mall, just south of Somerset at I-75 and 14 Mile. Adjacent to the Oakland Mall on John R between 13 and 14 Mile are several discount stores such as TJ Maxx and Marshall's where you can also find good bargains.
Somerset is very, very upscale. Oakland Mall and surrounding stores in its area are more mainstream-- Target and the like. They're not too far from each other.
Great Lakes Crossing is 20 miles/20 minutes (when there is no traffic) north of Oakland Mall. Birch Run is yet another 50 miles/50 minutes north from Great Lakes Crossing.
You park your car once, then walk around Great Lakes Crossing. You drive around Birch Run, since the store are arranged in clusters and rather spread out.
If you are familiar with stores and brands, these lists for each might help.
My vote would be for Great Lakes Crossing. It is my favorite outlet mall in Michigan. I assume you have a rental car or access to a car as you will one to get there. Somerset is neat to look at but I find to expensive to shop at. I still love the moving walkway over the highway!
Thank you guys for all the informations. Looks like Great Lakes Crossing is closer
to the hotel.
If you want to shop at specific stores make sure to sign up for their email/text messages. They are sending a lot of discount coupons/codes as this is back-to-school shopping time for kids in Michigan.