It's true that comparative advantage theory is better for trade, but I wouldn't necessarily say that it's better than other theories.
The reason that the absolute advantage theory is not as favored as it used to be is because it leads to less trade. Absolute advantage theory encourages only producers with an absolute advantage in a good to trade. So, for example, only one manufacturer or one country would produce shoes because it can do it cheaper and more efficiently than anyone else. But this means that other countries will have to produce something else and they have to buy shoes from that country alone.
It is generally accepted that trade is beneficial for everyone, it helps economies grow, it encourages development and gives people access to more goods. Comparative advantage theory allows everyone who can produce a good at a relatively low opportunity cost to do so. So there is more trade, and more growth.