In my opinion if you're out for performance the TT majorly trumps the Whipple. You could probably argue it's better for less shifting with the massive low-end torque, but that torque isn't friendly with 1st and 2nd gear. Obviously it is significantly cheaper, a lot closer to plug and play, and closer to the stock spirit of the car. TT's feel different than the stock car. The Whipple will feel like a GT with the power turned up to 11.
The beauty of a properly sorted Turbo system is that you can manage the power output to make it usable. Having 750-800rwhp with a huge amount of low-end torque is useless in 1st gear on street tires. With the twins you can go 600rwhp in 1st, 750rwhp in 2nd, 900 in 3rd, etc, etc. I drove one of the 800ish rwhp TT cars and it was just as usable as stock, but acceleration was absolutely furious once it got going.
Additionally, a TT car will make much greater power at the same boost level. For example, at 20 psi on 100 octane a TT car made 952rwhp through the stock exhaust. Highest I know of on a Whipple is 771rwhp at about 23psi. You can get in the 700s with the same amount of boost a stock car runs with twins. I'd rather run 15# and get 750 than 22# and 750.
But of course there is the issue of price. You have to pay big bucks for a TT kit. Any tuner taking on the responsibility of screwing around with a 170k car is going to need to make sure it's done exactly right. The stakes are significantly higher when you're dealing with a motor that costs more than a Corvette. Plus, there's the extra hardware and the fabrication and whatnot.
You can't go wrong with either one. Just depends on your goals and budget. Either will haul ass and look good under the clamshell...