The chapters are different, and you should go to one which suits you best. The Little River is the most active to my knowledge, ie Troutfest and meeting consistently. The Great Smoky Mountains group has some people who are active, but the chapter is not doing much these days. As for the Clinch River; similar (though someone may correct me) to GSM in that they have some active people, but as a chapter aren't doing much these days.
I would have to steer you toward Little River, though I am a member of GSM. They are active, and you will find that their members do more than just fish the park, or even trout for that matter.