Agree with many posts above.
When i bought my Eddie through a VW dealer they had fitted budget BCT ditchfinders, they were:
- noisy
- harsh ride
- front end would wash out in a corner
- under heavy braking the fronts would just lock up and slide
As soon as i changed them to Goodyear eagle F1 asy 2's, i instantly thought 'thats better, just as the car should have felt', they were quieter, gripped far better and didnt lock up when braking.
For me the biggest difference would be similar in comparision to summer vs winter tyres. Its not only about traction but braking.
With winter tyres you have far more confidence, under braking, even just approaching a junction at 15-20mph, summer tyres would lock and skid, winter tyres you come to a controlled stop. Using cheap budget tyres under heavy braking felt the same.