When something does interest me with the story in the game, I tend to not get it from cutscenes. I go read wikis. Researching specifics that interest me is what I prefer rather than sitting through cut scenes. The stereotype that WoW has no story and therefore its players must be out to ruin FFXIV's story is pretty insane, though I've seen it said quite a few times lately.
Wow has story, but it is very shallow and players tend to turn away from the lore since they must invest money and time to read the books and reading the wikis. The story for wow has sadly become a shadow of its former self like the game since Wotlk. The story has become a mess with time travel and lack of character development between the heroes and villains with terrible lore choices that the writers have taken, especially with the end of the new raid in patch 6.2. Players from wow may not be interested in the lore and some may be. It depends how they like their story. Dark or light?