The 18" wheel will be fitted with a lower profile, wider tire. This gives you the same overall diameter so as not to throw the speedometer off. The lower profile tire will put a wider contact patch on the ground and the shorter sidewall will quicken the steering response. All other things being equal you should expect sportier, better handling from the 18 inchers.
There are some trade offs though. First, the shorter sidewall will reduce the amount of cushioning the tire can provide and may degrade the ride quality a little. Secondly, the 18" low profile, high performance sized tires may not provide as much tread life as a higher profile all-weather type tire. Lastly, shorter, wider tires can be worse for traction in snowy weather, particularly if they are a ultra high performance type tire.