That's kind of an apples & oranges question. Showing in what events? What disciplines?
Yes, quarter horses tend to make a great all-'round horse (although different lines have been bred/overbred for various disciplines these days), but you wouldn't take one into a gaited class.
TWH's tend to make fantastic pleasure horses & show horses in the disciplines for which they've been bred & developed, but I wouldn't throw one in a show pen full of cattle against a QH from good cutting horse lines & expect it to perform the same. That would be like expecting to turn a Belgian Draft into a world-class showjumper, or a Friesian into a typey, fancy hunter that cleans up on the A circuit.
Awesome thing about all of it is, there are a LOT of great horses in the world, regardless of breed.
$.02...
It's nothing that personal, just your overall personal preference... What is your favorite?