Which computer package is better, GAP or SageMath, for decomposing an irreducible representation of a (simple) Lie group $G$ into representations of a Lie subgroup. I am most interested when branching to Levi, or parabolic, 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).

$\begingroup$ SageMath includes GAP as a standard package, so in theory, SageMath can do anything GAP can do. In practice, SageMath can easily do anything from GAP for which someone has written an interface. It can do other things, but not in as seamless a way. $\endgroup$ – John Palmieri Mar 11 at 17:00
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://wwwmath.univpoitiers.fr/~maavl/LiE/

$\begingroup$ I haven't used it, but SageMath comes with an interface to LiE. Run
sage i lie
to install it. In a perfect world, this would interact well with the rest of SageMath. $\endgroup$ – John Palmieri Mar 11 at 16:58