We have had several TWH and MFTs and both are great horses. We started with the TWHs and transitioned to MFTs over the years. For us the change was mostly due to the type of country we ride in. We ride lots of rough trails when we are even on a trail. Our TWH's were wonderful and had great smooth gaits, but they couldn't gait very well in rough county. On a dirt road or smooth trail they could really fly. In fact our fastest TWHs were faster than our fastest MFTs.
What sold us on the MFTs is that they can do their gait in rough country much better than the TWH can. In rough country we found the TWH's had trouble keeping up. Both generally have great temperments, are sure footed, great stamina, and have good fast flat walks.
You can find nice heavy boned stout horses in both breeds as well, so it really came down to which breed could perform the best in rough country day after day. We have a few TWH's we have held onto because they are exceptional individuals but generally the MFT's out perform the TWH's in the rough country we ride. We have also found them to be a bit more versatile all round horses.
For most applications I think anybody would be happy with either breed. If I lived in the flat lands and planned on purely trail riding I would possibly lean towards a TWH. Where I live/ride in the mountains I prefer the MFT. Both are great to ride and truth be told you may be best off finding the horse that best fits your riding level/desires regardless of breed as both are exceptional.