The main attribute is as coxw says, the Leon Cupra has alloy running gear components to reduce weight of the unsprung components where as the FR uses the usual steel components.
As well as the obvious weight advantages, the alloy is more compliant to the stress forces on the road but also recovers much faster too. It shares these alloy components with its VAG stablemates the Golf Edition 30 and Audi S3.
Then as djhorace explains the dampers, springs,bushes etc are all uprated compared to the FR.
I have an official press pack given to me in 2007 when myself and m0rk went to the UK press launch. It goes into a little more detail I think, I'll dig it out later anyway to check.