Width and Height

I'm wondering what (if any) performance modification there is when you:
1) use a wider tire
2) use a tire with a larger diameter

Wider tires will provide a larger contact surface, providing better dry traction. The offset of this is in rain or snow, where you have less weight per area on the contact patch and you could end up with worse traction.

If you mean a larger diameter wheel, ie 18" vs 15", but keeping the overall diameter of the tire the same, you get a smaller sidewall which will flex less when cornering giving you better handling. The offset here is ride quality, because the tire's sidewall absorbs some of the impact from bumps and potholes.