Spoiler free*
Aside from the story, the game is an improvement on the first in every way.
The voice acting, animations, music, locations are surberb. The gameplay is a much improved and expanded version of the first. The graphics and UI are improved.
As far as the story, I personally didnt expect a repeat of the masterpiece the first game was. This story has a larger cast and a few more moving pieces. Its not anywhere near as good as the first, but it certainly has its moments that can easily rival it. Regardless of the weaker plot and narrative, I find this to be a more than adequate sequel. I never saw the need, nor even wanted a sequel to the first, but I certainly appreciated and enjoyed being taken back to The last of us' beautifully crafted world and spend some time with some old friends.
In summary
Its a very well polished(development and gameplay), upgraded sequel to the first with a shallower plot.