rylla
Shortly I see the main difference between these 2 cards as
in the 8 of Cups you are moving away from something that you used to love/like (or be content with) but it's no longer satisfying to search for something better
in the 6 of Swords you are moving away from a difficult situation to something better (basically, your situation changes in better)
so the motivation and circumstances that pushes you to move forward are different
ETA I haven't read the other comments yet (I'll be doing it now), sorry if I am repeating some ideas already mentioned above.
in the 8 of Cups you are moving away from something that you used to love/like (or be content with) but it's no longer satisfying to search for something better
in the 6 of Swords you are moving away from a difficult situation to something better (basically, your situation changes in better)
so the motivation and circumstances that pushes you to move forward are different
ETA I haven't read the other comments yet (I'll be doing it now), sorry if I am repeating some ideas already mentioned above.