Ride feels firmer with lower profile than the 55 but too low a profile and it can struggle for traction with regards to bumpy roads. At any rate, the profile of your tyre is not the reason why there's a lot of understeer. Wider tyres would be more important than thinner tyres if your struggling for traction, also the tyre your using makes a massive difference, not sure what tyres your using but try a quality tyre like Michelin pilot sport 3 etc.
A good set of coilovers like Kw variant 2/3 or bilstein b16 pss9, front and rear antiroll bar and front and rear strut braces and a aftermarket LSD would help.