One is reflex. It is about muscle memory. The goal is to be able to react to a certain situation by reflex action. Such training entails repetition of a single set of motions over and over again, until the body is able to carry out the exact motions without thought. When a trigger occurs, the body goes through that same set of motions as a reflex action.
The advantage of such training is that it eliminates the need for thinking during application. The disadvantage is the need for a very very huge repertoire of "set pieces" in order to be able to handle different kinds of situations. And the more "set pieces" there are, there more time is needed to train, since it takes thousands, if not tens of thousands, of repetitions to hone such movements into reflex actions.
The other was is response. The goal is for the body to carry out the full response as commanded by thought. Such training entails training the body to respond to the brain, to train the brain to be able to fully control every single movement of every single body part. Time is spent on training the body to precisely execute the commands from the brain. The keyword here is precise. Thus, when a trigger occurs, the brain immediately analyzes the situation, then tell the body exactly how to respond to that trigger, and the body precisely carries out the response.
The advantage of such training is that it is not limited by one's repertoire. The brain can think of responses for situations which is has not trained for, and command the body to execute the responses. The disadvantage is the the brain is now involved, so there is a need to train the brain to think, by feeding it scenarios, allowing it to analyze those scenarios, and then forming a set of principles on how to react. There is also the time needed to train the body to be able to precisely execute each command the brain can give.
So which is the better way?
Personally, I think there is no way to compare, no way to judge. Different people have different preferences, and what works for me may not work for you. The common thing, though, is training. Both ways require a lot of training, and is only effective through a lot of training. It is often said that hard work will not betray you, and in this case of training, I can only agree.