Oi! Leave Nankangs alone!
Back on topic though, for anyone that says they lost in on a round about or a similar incident, you can't blame it on the tyres (Unless they're bold) It's down to the driver pushing it too hard or not knowing the cars limits.
Yes tyres, as Stevo says, will improve the speed you can take a corner, but at the same time - If you're driving normally, budget tyres are NOT going to kill you unless you drive like an idiot.