The story is good -- It might seem like there's less of it, mostly because it's not integrated into overly long cutscenes this time, they trigger as you build your army and base and do missions, and as you listen to audio tapes (which is essentially the equivalent of the codec calls this time) both optional and main missions. The interesting thing is that the fate of certain characters, like say Quiet or DD, are optional, in regards to what happens to them it's up to you. 

Basically, the game has taken all of the best parts of Peace Walker and nearly perfected them.. excluding the lack of co-op but there it is.
The story truly kicks off a little later as you build your base.