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.



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).


