The first symphonia is almost better than dawn of the new world in every aspect. I think you'd be a bit lost with the plot and allusions to the first game if you never actually played it. Dawn of the new world was made (in my opinion) to directly cater to fans of the first game.

 

Well, they actually explain that to you in New World, but you probably just didn't understand the reference. They go all the way around the world(s) to...

Warning: Spoilers inside!

...regenerate the world. Of course, they discover there's an entirely separate world -- Tethe`alla, which you don't learn about until about midway through the game.

There are, however, other great story twists that aren't harked upon in New World, and I'd say it's definitely worth going back and playing the first game. I prefer the controls in New World, but the battle system -- with the S and T-type techs and ExSpheres -- is much better in the original. Story, combat (except for the absence of free roam), dialogue, gameplay -- everything in the original is so much better than New World.