When sequencing actions (doing A after B)
～た後で implies that the actions are independent.
仕事が終わった後で行く I will go after work lit. (after the work has ended, I will go)
～てから implies dependence: v1 can only be done after v2 has been done.
仕事が終わってから行く I will go after I finish work (I cannot leave before work is finished.)
Youtube: Miku Real Japanese - The difference between てから and たあとで