I love the friendly and colorful animation of the original 1987 TMNT series, but I kind of like the darker and more serious look of the 2003 TMNT series a little more, both have left me with a sweet taste in my mouth so I can't complain about either's animation. When it comes to the fight scenes and battle sequences I do have to give 2003's TMNT the nod, it was more action based and a lot more mature in that aspect, in the original there was too many silly ending's to fights that took away from that fact that someone actually defeated Shredder or whoever they were fighting.
I do love the 2003 series to death, but when I strip down both shows I find myself enjoying the original slighty more even though the animation isn't as good and the battles are slightly cheesy. I think I'm a sucker for nostalgia and TMNT 1987 was a massive part of my childhood and 20 years from now I'm going to look back at the classic TMNT series and the 2003 TMNT series and remember having more memories with the original, but a big part of that could be the time period in which I was watching them. Obviously times were a lot less stressful as a child than as a 20 year old who had a job and school to juggle so that may have something to do with things, but still, regardless of time era the original edges out the 2003 series by a tiny margin.
I'm all about both series though, TMNT is just an amazing franchise (Fast Foward excluded).