Another thing to consider is that tyres are THE ONLY CONTACT your car has with the road, so even if you have the best suspension, steering, brakes and drive-line combination you could possibly achieve, then it all turns to sh!t if you have ordinary tyres on the car.
If you can afford to spend a bit more, it may well save your life one day, so it's a worthwhile investment. And don't bother comparing brand against brand, it's more "accurate" (I can't think of a better way to describe it right now, but...) to compare TYRE against TYRE.
An example: Falken make two tyres which are at opposite ends of what they may consider "performance" tyres - their Ziex range is total crap (I know this from experience), yet their Azenis range has received lots of praise, and is one of the tyres I'll be considering when I update. Duncan himself swears by them.