"One plus to moving to Yor is that Russia won't see you as an immediate enemy. "
This means nothing though, as Russia has no power (and I mean literally no power) to stop you from convoying to Norway and moving to the Barents by Fall 01. It may galvanize him into forming different alliances but more likely than not, since Edinburgh is so common and is hardly alarming to Russia, it will have little impact. In addition, one can still convoy to Norway and move to the Barents Sea with Yorkshire, so it really has no difference.
"Can someone explain what else LIV-EDN gives other than the ability to convoy via Norwegian Sea, or is that a bigger deal than I think it is?"
Having options is so critical. Should you want to move the North Sea fleet to any one of the other SC's near it in Fall 01, it allows you to grab potentially 2 SC's (or at least weaken someone else by bouncing). If in a press game, North Sea can also support a unit into another territory to help an ally (like supporting into Belgium.) Since Russia also has northern openings that can work against Germany, having the North Sea bounce Germany in Holland, Belgium, or Denmark is amazingly beneficial in the right situations. Mind you, none of this is possible if it's sitting in Yorkshire, but almost everything you want to do with an army in Yorkshire is possible with it in Edinburgh too.