GAP versus SageMath for branching to Lie subgroups

I don't know GAP but Sage has a nice tutorial for branching and is quite usable. It is however, slower than LiE which is on the other hand quite "basic" i.e. it requires you to write the branching code (example is in its documentation).

I recommend LiE, which is a specialized software for computations in finite dimensional representations of semisimple Lie algebras. There is an online interface. See http://www-math.univ-poitiers.fr/~maavl/LiE/