I will pretty much agree with mtnmike on his advice. The cataloochee valley is a beautiful area and one that you will definitely love if you go there. The main stem of cataloochee can be a tricky place to fish and i would have to agree that it is probably because of the larger concentration of brown trout. It is definitely a humbling stream to fish. Don't let that discourage you, though, because i have personally seen some very large fish in there. Even though you said you would be going in the spring, i would think the best time to fish it would be early in the morning, late in the day, or when it's cloudy and/or rainy just simply due to the fact that you could conceal yourself better. One of the better days i had on catalooche was a cold, rainy day.
I have fished palmer several times and have most always had better luck there than cataloochee. The average fish that i have caught also seems to be pretty nice sized, around 10", but that may just be luck. I have caught mostly rainbows out of here but you start running into a few brookies when you move farther upstream. I have also ran across several larger sized rainbows in the lower portion in the 14-16" range. The headwaters of palmer (lost bottoms, pretty hollow, etc.) offer some excellent brook trout fishing. I have only fished pretty hollow, but am planning a lost bottoms trip very soon. If i was backpacking and staying, i would stay at campsite #39. That campsite allows you easy access to palmer, pretty hollow, and with a short walk lost bottoms.
One other area you might want to consider is hiking up big creek. It's not that far from cataloochee and is a rough and tumble mountain stream it's entire course. I haven't fished it, i've just hiked it, but it looks fantastic. You could stretch your legs really good and hike up to campsite #36 and probably have the stream pretty much to yourself and you would be into some good brook trout water. I don't think that this area receives much pressure, but i could be wrong. I have heard some good things about several of those feeder streams above campsite #36.
Hope this helps and let us know what you decide and how your trip goes.