The long-term outcome of all mantras is that they lead to samadhi. Some work faster than others, which, ironically, is the point of advanced techniques: the dive is more shallow, so the progression to samadhi takes longer.
So that doesn't explain the striking difference between TM and other mantra-based methods. It's not the fact that a simple, fast-working mantra was being used. If that was the case, then other practices would show the simplest state of awareness slower, but instead, they show it LESS, the longer people have been practicing. L