There's LOTS of story telling in WOW, but I haven't played it since just before Cata. The model updates look pretty good though.
Cataclysm was truly cataclysmic. many of the stories you remember (and a lot of those stories I STILL remember)... no longer exist in game. they changed content for lvl 1 through 60 so much its just... sad. you may enjoy the changes. you may not. different people had different experiences. for me, personally ... most of the Cata stories just didn't work. though I'm trying to give them another chance by playing through all the starting areas that I skipped on a trial account. its... slow going :P
storytelling in WoW though is less interactive than in SWTOR. and very reading dependant
almost no voice overs, with exception of cutscenes you are spectator in, rather then active participant. some people prefer it that way. to each their own