Firstly well done for considering cross training. Either of these would complement your current training.
It is true that you should examine each school and teacher first.
I study Shotokan, my wife Tae Kwon Do.
On the surface both arts are quite similar. The difference comes in how the techniques are applied and the overall emphasis.
Although TKD is renown for its powerful, high kicks, but it also has punching, striking, grappling and throws.
Shotokan is probably one of the most popular forms of Karate and generally has a more traditional approach.
If you have any more specific questions there is a TKD forum, read other entries in this forum, or post them here and I will try to answer them.