But how can the magnitude be different in each case? If the magnitude is different surely I must be feeling it differently if I travel in a rotational frame than a translating frame?

Anyway to convince myself that it is indeed the case?

But physically does it means that the way the car in straightline feels the velocity of car in the curve, is different from the the way the car in the curve feels for the car in straightline? It's mathematically correct..But little counterintuitive

Please look at the posted examples

What I meant to say is the local coordinate fixed on the second car moving along the curved path is rotating with respect to the centre of rotation.

Are you sure? The second car is moving in a curved path so there will be a rotation effect for sure.