Once mounted on the rim, both size tires are the exact same circumference. The only difference is that the 19 inch tire has a shorter side wall. This makes up the inch difference in diameter and makes the tires the same once mounted. The 19 inch tires are generally a bit lighter in weight than the same tire in an 18 inch size.
Some say that 19 inch tires are more prone to pinch flats. I've never noticed a difference. Other than that, most riders would be hard-pressed to tell ANY difference in how the tires handle. I sure can't, and I've ridden and raced for 15 years on both sizes.
Make your trade and don't worry about it, as long as the tires you want to use are available.