Is this your first Musou and/or Dynasty Warriors game? (Specifically in the Three Kingdoms setting)
I think there's enough story from the XL stages to get a feel for some of the characters, and you'd be missing out on the bigger story though.
I have DW8 Vanilla on PS3, DW8XL Complete on Vita.
I honestly preferred the DW7 story more so I'd recommend that if you wanted to experience the story.
There's no real problem if you don't care about the story, because you can play all the other modes instead. The story modes are pretty long though.
Basically what you got isn't really a fraction of the game, it's an expansion of the original DW8's story mode. "Various characters not playable or have a minor role within Story Mode star in an all new storyline of hypothetical scenarios, where they are 8 stages long and focus on additional battles or alternate versions of existing ones. There is also the option to unlock 'Other' scenarios after completing other objectives for the main 4 kingdoms. "
You can't play as all the characters in the story mode in XL only.
http://koei.wikia.com/wiki/Dynasty_Warriors_8:_Xtreme_Legends