I have used both. My original experience was with the Mtn Trainer. I really liked how they felt on my feet, but after wearing them for several hours, I started getting excruciating heel pain. Not sure what it was related to. Several weeks later I wore them again and had the same problem. I moved over to the Alp Trainer and haven't had any problems.
That aside, here are the differences between each. In my opinion, the MTN trainer felt a little more like a traditional hiking boot. It had good support and a good sole. In addition, it appeared to be a little wider than the Alp Trainer. I would classify the Alp Trainer as more of an ascent shoe. While it can certainly be used for hiking, the sole and narrowness of the shoe make it suitable for rock hoping and bouldering a little better. The Alp Trainer does tend to be a little narrower so if your feet are wide this might not be the best fit.
One other major difference right now is that last year's color of the Alp Trainer are $100 cheaper than the MTN trainer on Backcountry