I highly suggest that you watch Prince of Tennis and its National Tournament OVAs before watching New Prince of Tennis.
I loved the original Prince of Tennis (and National Tournament OVAs) and finished it in about three weeks a while ago. The New Prince of Tennis is had a completely different atmosphere that I didn't expect.
Story : The story was acceptable. 50 middle school representatives from the national champions go to the U-17 Japanese representative camp against high school students. I thought it was interesting at first, except when that started to change further in. Then, the story started going downhill from there. I nearly
dropped it because it had nearly nothing to do with tennis. There were barely any tennis matches in the second half and I started to lose interest, but then regained it in the last episodes.
The comedy wasn't as great, but it was there to an extent.
Of course, I think that New Prince of Tennis would have been better if it had more episodes to work with. Most of the matches weren't that bad but it would have been more climatic if it were longer.
Art : Nothing much to say.. the art is much more modern, brighter and sharp, which is an improvement.
Sound : To say the least, I didn't like the opening and ending themes to New Prince of Tennis. I thought that it didn't fit properly at all, even though I had listened to them multiple times. (I absolutely loved most Prince of Tennis' opening/ending themes). The seiyuus' did their job but they weren't superbly brilliant.
Character : It was nice to see the old characters back with some development and not just Seigaku's. However, others were almost completely left out. A lot of characters just said a few sentences. New characters weren't that intense either since they didn't show up all that often.
Enjoyment : Overall, it was an arguable anime. I did enjoy it but it didn't live up to my expectations.
Overall : I can't give it a higher score for New Prince of Tennis since it screwed up a bit at the midpoint of the story, and it didn't have an overload of tennis. (What would you expect? "New Prince of 'Tennis'").
New Prince of Tennis is worth watching if you want more material, but don't get your hopes too high if you think it'll be as good as the original. To me, it definitely is a let down and it didn't have a huge impact on me.