I would pick a roots style screw blower for a high hp car that will be tracked, but it's not going to make 1000 HP. Oh, they can on a dyno with ice water in the liquid intercooler, etc. but in a driving situation with heat soak they really aren't going to be 1000 Hp.
With that said I'm sure someone will post up an example to prove me wrong. Turbo(s) are by far the easiest way to that goal with a car that can run like a stock small block when cruised. Not ideal usually for the track stuff as they can be fun to drive fast, but they are trackable. A good electronic boost controller to control how the boost ramps up vs rpm and gear would be a great idea. I had several laps with Stielow driving the Mule, and it worked quite well; the boost was turned down a bit though, not on "kill". Then again, that's Stielow driving............
My ideal engine for my next car would likely be a roots blown LS. I figure it can make an honest repeatable 750-850+ HP, and that's plenty. Boost is instant, and a bit easier to drive fast I believe.