Correct.
aldazo, you can actually test it out with your current controller.
Take your standard Dualshock 3 and simply plug it in as if you were charging it. Now play some matches (preferably offline) and you will notice that the inputs will be read faster as opposed to wireless.
The reason tournament players do not use a PS3 pad is because they are not tournament legal. The home button can cause serious sync problems and could potentially screw up matches in progress. Removing the battery / converting the PS3 pad to only read a wired connection is an option some people use but bigger tournaments (such as EVO) do not accept this as a legitimate wired controller and forbid them.
bettyswallaux, it was mentioned before, but a good (under $50.00 option) is a PS2 Pas with a X-BOX 360 to PS3 converter.
A stick option is the standard Street Fighter IV Fightstick which can be purchased quite cheap these days. Out of the box, the components are not the best quality but it's an easy stick to mod / customize; if you feel comfortable playing on the fightstick and want to take it to the next level, you can easily swap out the buttons and joystick for good quality SANWA parts.