Personally? No. Don't read the manga.
The manga is good. In fact it's a lot better than most of the anime in the sense that the anime wasted a lot of time with nothing but static scenes where they were just playing music over a few lines of monologue...
...but the anime gives a very distinct sense of closure and completeness. It ends on a heartwarming note and lets you imagine the rest.
The manga, as far as I know, is still running. Meaning more and more stuff gets stacked on top of that.
Personally, I'm a fan of shorter, more intense and complete feeling series than long and drawn out series.
If you don't feel the same, then by all means read the manga. As I said, it's still good.