Actually the reason I brough the Almoravids and not the Almohads is because unlike them the Almoravids also went south and destroyed a black African empire, I think Ghana. In Iberia they came invited by the Taifas as protectors, but decided to backstab their kings and just annex them. Then they moved onto the Christian kingdoms and while their highly effective light cavalry, horse archers and camels won some key battles they failed to make many territorial gains because the country is mountainous and too fortified. As you can see the story is highly reminiscent of the Mongols, just in a minor scale; even the existence of castles, which in Spain were perhaps more common than in any other part of the world, is often brought up in alternate hsitory discussions about why the Mongols couldn't have taken over Western Europe.
Now the differences:
The first one is religion. The Mongols were followers of several different religions and Genghis Khan was a pagan himself who gave no though on the religion of his subjects and allies. The Almoravids were on the other hand, universally followers of their particular branch of Islam (though not nearly as zealots as the Almohads, but I think that's only a matter of degree).
The second is the degree of destruction involved. Passing entire cities to the sword and destroying everything including water works because their rulers didn't surrender when told and all that, like the Mongols did. Any Berber state/group/dynasty understood the value of cities and infraestructures as not just deposits but also generators of wealth, which doesn't seem to be the case with the Mongols, at least early in Genghis early reign (and for the whole duration of Timur's, but in this case it was probably pure sociopathy on his part rather than cultural differences).
On the other hand the Almohads mostly spread later along an east-west axis rather than a north-south like the Almoravids and reached eastern Libya; they even brought an army of Turkish mercenary archers employed by the Egyptians that they had captured in a battle there to Las Navas. This use of multiethnic armies (even if the top leadership was not) with new peoples being added with each conquest as their troops advanced is also reminiscent of the Mongols.