I don't think tennis shoes are good for badminton because the movement patterns are totally different. You better take any indoor sports shoe (Asics has good ones for example) before considering a tennis shoe.
Generally, with tennis shoes, your feets are higher off the ground which is no good for badminton games.
Badminton shoes are designed for the feets close to the ground and still have enough cushioning.
Tennis shoes thread/sole is also less gummy/tacky.
When I first got back into badminton...I bought a Nike indoor court shoes. It was OK at the time. But ever since I bought my Yonex SHB 102 shoes...I'm like a half-step quicker. It was that much of a difference (to me at least).
So listen to the posters above...get badminton shoes.