Time of trainig vs time of prediction, which one is used during classification algorithms comparison?
I get this answer, if it may helping you or if you have any other information to add :

If we are talking only about computational time then prediction time is more important if the training time is finite and accuracy is comparable. Training time can be handled easily by using a good machine.

This is important because any machine learning system is expected to generalize or at least have higher accuracy on the testing set. To achieve this better performance training time is often not considered. If one algorithm has significantly higher training time but good accuracy on testing test then it is considered better because once the training is done, the algorithm doesn’t need much tweaking. Obviously in this case we assume that the training time is finite which can be reduced by using a better machine.