A sidewall is nothing but "unsupported" rubber. The more sidewall you have, the more it will flex. On 175/70/14 tires a Capri will feel like a big boat when you're trying to maneuver.
That's why folks go to a wider wheel, and less sidewall for better handling (there is a limit to this, too small a sidewall can be detrimental to performance, but it's pretty extreme)
Of course this is only my recommendation