I haven't purchased one yet but was strongly considering purchasing the Barton towards the end of month. Now I'm second guessing my decision since a lot of people recommend the MGW.
I had a chance to see the Barton setup this past weekend at the American Muscle Mustang show. It is a very nice setup that is completely customize able. It can either be trans mounted OR body mounted. You can completely change the spring setup in the cartridge so it is more like stock in terms of pressure side to side or you can make it extremely solid and precision oriented. It is a very nice setup and completely made in the USA. If you have not seriously looked into the Barton setup I would. The entire package can be had for $475 and it even comes with a shift knob in white or black.
I have an MGW. The owner installed it for me (I'm only a couple hours away from their location). It's a wonderful shifter. I've also driven a Steeda Tri-Ax and I think that is great. The Barton, if I can speculate, has a shorter throw and I constantly see people switch from it to an MGW or Steeda. MGW is a full shifter replacement and is transmounted. Steeda is not a full replacement, but nonetheless excellent and easier to install; plus you can keep the pull up to reverse functionality that you give up with MGW. I find, if I'm honest, MGW's push down to reverse functionality really annoying, but I live with it. I've never shifted better in my life (in other words, I've made it to being able to actually beat a car for once in a competitive drag race (specifically, 2016 Camaro SS automatic... word).
I have the MGW and love it. Had one on the old 07 GT and loved that too. Tried a Tri-Ax on someone else's ride and it was a nice piece with a good feel. Hear great things about the Barton but if you want the best shifter available, the MGW cannot be beaten purely because of the engineering that has gone into it. It solidly mounts to the transmission (AFAIK it's the only aftermarket shifter that does this) removing the remote mount feel of the stocker. This has positives and negatives. As it's solidly mounted there is a little more vibration transmitted through it but the supplied Dynamat/foam pad takes care of most of that. On the plus side the shifter will move very slightly in line with the torque the engine puts on the transmission so your synchros will thank you for it. Never missed a shift since install and the throw is absolutely perfect now. Not to mention MGW customer service is great. You won't be disappointed.