We've been to both many times and I absolutely recommend Garden Grill. We're a family of five with three boys, and Garden Grill has been our arrival night tradition for years. It's definitely one of our favorite character meals at WDW. Here's why:
1) Food. The food quality at Garden Grill has improved significantly in recent visits - everything has been fresh and flavorful. I especially enjoy the bread, salad and mashed potatoes. The sweet potato fries they bring out with the kids' items are great.
2) Service. We absolutely prefer family style service over buffets. We still get a variety of foods, but the servers bring everything to our table so we don't have to get up and down, juggle plates, miss characters and flag them down to come back to our table, etc. It allows us to have a conversation with our boys instead of getting up and sitting back down at different times.
3) Characters. We've always enjoyed quality character interaction at Garden Grill. They never seem rushed and we usually see each character at least twice during our hour-long meal. Once, our oldest son forgot his autograph book and Pluto made a point to return to our table an extra time to sign. If your kids don't respond well to the characters, they do a nice job of just waving and moving along (this works especially well if you are seated in the lower level booths - see below.)
4) Atmosphere. We always request a lower-level booth, which makes Garden Grill more quiet and less hectic than any other character meal. (Ohana breakfast right at 7:30am comes close, but in a different way.) In the lower level booths, you still see all the rotating scenes from the Land ride, but that's it. You don't see other diners or the beverage/bus stations. Also, this level is great for photos with characters. If you seat the kids at the end, they can jump up for photos without chairs getting in the way, and then the background is from the Land ride. The upper level is OK, but we always had kids fumbling over the chairs and the 70s wallpaper was in the background instead of the Land scenes.
In our experience (and we've tried it several times) Chef Mickey's is quite different in terms of food quality, service, character interaction and atmosphere. I do still recommend Chef Mickey's to those who are looking for something in the MK area and really want to see the Fab 5 in their traditional attire all at once. And we do have friends who love the food there, so it's not absolutely terrible. I also think it's fun to try Chef Mickey's at least once, because it's definitely a classic. But overall, we prefer Garden Grill.
Good luck with your decision and have a great trip!!!