If you're a fan of classical music then you'll appreciate the jdrama much more
In general the performances are superior and the arrangements are much more unique and interesting than in the anime, the drama did a much better job of conveying the unique personality and playing style of Nodame and the S Orchestra.
The anime used stock recordings of all the pieces whereas the drama actually used a real orchestra and musicians from a music school for authenticity.
In addition the drama has a lot of interesting visual effects and props used to make it feel more like a manga come to life than just your standard drama, and Ueno Juri and Takenaka Naoto do a terrific job of bringing Nodame and Streussman to life. They steal the show every time they're on screen, and Takenaka's imitation of a gaijin's accent is hilarious if you're familiar with japanese.
I love the anime, but the drama exceeds it on every concievable level, though most denizens of /a/ are too put off by "3D Pig Disgusting" in order to appreciate it fully.