I've raced against but never driven on the Federals. My base MINI came with 15" Conti Premium Contact 2's. They were more nimble but not nearly as fast against the clock as 16" Dunlop Star Specs.

Steering effort will be less with full depth tread than worn tread. Full depth tread is also subject to squirming under heavy side load.

I currently have three sets of 16" wheels for my Roadster S with up to five pounds difference per corner. I can't say that lighter is better for cornering. Too many variables to say what specifically accounts for the changes.

 

there's a reason race cars run a soft compound virtual 'slick' on a dry track