CFA is the oldest cat registry in the US. They are more strict with their standards (more extreme in a lot of cases) and less likely to accept new breeds/colors.
TICA is one of the newer associations and accepts a lot of new breeds/colors, etc.
If you have one of the more common breeds you would register in both. But if you have the newer breeds, you register with TICA.
When I was showing cats, I showed in CFF, ACFA, ACCE, TICA and CFA...all of them have their pluses and minuses. You should read over both associations websites, take a look at their breed winners, go to a show or two for both, and then decide which suits you best.
For me, with a new breed, I showed in both, wanting to promote and help the breed advance in both. I personally found TICA more friendly, liked their scoring system better, found it a bit less political (though politics is in every association) and perhaps because they accepted my breed for CH competition first, spent more time there.
I recently went to a CFA show in Ohio. My first experience. But it seems most people agree TICA is more friendly. Since I havent gone to one of those yet, I will let you know. I did have an awful lot of fun with the girls that were showing their cats. Its all a little overwhelming trying to figure out the way they do the judging. But still a lot of fun! There is one this weekend in Monroe Michigan...I am going to go on Saturday with a friend coming in from texas.
I wish there are TICA base cat show in my country because I want to see people fancy munchikin and bengals here in Malaysia. Since Jan this year, only CFA shows ..