I'm kind of new to tarot, but here's what I think:
The 6 of Swords is the kind of moving on that is tinged with a very acute sense of nostalgia. Querent would have a difficult time getting "unstuck" from this loop of nostalgia, even though they are physically putting distance between themselves and the relationship.
8 of Cups, on the other hand, seems.....more stern to me, if that makes sense. It is more permanent in the way that it doesn't give into nostalgia or crying or etc that the 6oS does. It's just kind of this cold, calculating statement: "Well, I did my best but it wasn't enough, so oh well. End of story."
So, to simplify a bit....6oS is kind of the weepy, clingy kind of "moving on" while 8oC is more hard-hearted, independent kind of moving on. Also the 8oC seems like a quicker way to "get over" the situation.
As I said, I'm not really good with the cards yet, but that's my 2 cents.
