TTs are sick for small waves if you have a quick, floaty, little wave kite like a drifter, reo, religion etc but if you're on more a freeride kite you're better off on a surfboard if only in that it will help you stay on the wave while your kite's 'mushing' about.
Your big floaty SB, is designed to stay on a wave & cruise the city beach slop so ya don't have to be evil kenevil on your TT ta tighten up the lines!
So your board choice depends largely on the type of kite your packing.
In bigger scarier mush I found the TTs nice enough even with not so gr8 kites because once you're planing up to speed on a bigger face, you can fairly easily hold that speed due to the wave momentum & have a sick run if the winds right....if it's not you can surf real fast straight at the kite an then it's back to get a wave kite! When u've done that, you can take out your mum's
ironing board and still rip, but try to get one with a little more rocker than your normal IB if you wanna send spray over those SB riders who dare to ride next to you