Thanks for playing the game! The branches are fragments for player Stats upgrade, i.e. attack speed, range and etc. Another type of "choose 1 from 2" reward drop is weapon reward. You can keep choosing the same weapon and become more powerful. And thanks for the suggestion on critical hits! There is indeed one weapon, the green Fantian Seal, can deliver "rooted" effect which will slow the enemy for half a second.
Again thanks for your time playing it!