If you can afford it, do it. The STi is a superior animal even though I have never driven one, I know it to be true. I have driven the WRX hard and fast and broke it lots! The STi would cope much better than the WRX with this type of driving. As for the closer ratios of the 6-speed for cornering, possibly true, however, with a remap and bigger turbo, you will feel an enourmous difference in the mid-range; perfect for pulling out corners without down-shifting.
The other option you have, which is MUCH cheaper, is to get that bigger turbo, and go for a remap with a sports cat. If you're not going to track it, the gearbox and internals should handle it, but the risk is greater than with the STi.
If I hadn't thrown so much time, effort and money (especially money!) sorting my WRX, I'd be looking at an STi for sure. But there is too much history between myself and the "big guy" that I could never let him go.
Edit: I don't care much for those semi-slicks (Bridgestone RE070)! You can replace these of course