I have an LG French Door. I like it but I wouldn't say that I love it. But then again I didn't love our side by side or our traditional style either. This time we looked at pretty much EVERY model of refrigerator available in a 25 mile radius and picked the best one to match our needs.
My biggest complaint is that it is very difficult to find space for tall things. And since we shop at Costco and Sam's a lot it can be a problem. Also our freezer frosts over everything. I had the repair guy out and he couldn't find a problem but I think I may call again because I don't think it should be doing that.
I do love that the most used area of the refrigerator is at eye level, it is so much easier to find things.l
Here are the things that we looked for:
Ice Maker-- I had to have one but hated how much space they took up in the door. We finally decided to just go with an ice maker in the freezer, with no in door delivery. I actually have not liked our ice dispensers because the ice gets thrown on the floor, the drain tray gets nasty and my kids think it is a great toy. And they tend to break easily so my engineer husband hates them.
Drawers: This was a big deal. Many of the French Door models have a long skinny drawer (for meat and cheese) on the bottom, and the cover will open automatically as you open the drawer. But we found many where the drawer only comes out part way so you end up awkwardly sticking your hand into the neverland in the back to try to find things. I wanted the drawer to come out as far as possible. Also some of them would close on your fingers if you weren't careful (DH found that out!). And I wanted good quality wheels. Some of them were really cheap and it was obvious they would break easily.
Usable Door space-- think about what you like to store on the door and see if you will have enough space. Consider that most of your tall things (2 liter bottles, milk gallons, wine bottles) will have to go on the door, and then mostly small things in the other bins. I don't have enough room for even a large salad dressing bottle. Mostly I have small jelly and salsa type containers because that is all that fits. This is another reason I didn't want the ice maker in the door-- very little space for tall things anyway (without losing a shelf)
Door Alarm-- some styles (like my LG) have doors that don't close easily. You can't just let go with a small push like with other styles. So it is important to have a door alarm that you can hear if you don't get it shut all the way. Mine can also be turned on and off easily so when I am cleaning it out I don't have to keep hearing it beep!
Overall I do like it much better than our side by side. I have a large upright freezer and a traditional style refrigerator/freezer in the garage so I have plenty of other options for things and am not trying to fit everything into the kitchen so that makes it easier for me.
Good luck on your search!