I did loads of research on this when we moved into our current house a few years ago. We ended up going with The New England Shutter Company. Their shutters are wooden rather than MDF and personally I think they are right that you can tell the difference. They were really friendly and professional, and we haven’t had any problems at all with the shutters. Our neighbours also used them and have had their shutters for 15 years now. It obviously depends on your budget and also what you prefer.
The Traditional Shutter Company also seemed to be of the same quality, and I have two friends who used them and were very happy. Someone explained to me that a lot of the other companies actually source their shutters from the same supplier in China.