On the same runway (performance wise) a 200 (full noise and ICAO STANDARD DAY) is capable of carrying about 16T more than a 300, or at maximum derate a 200 will lift about 11t more. I'm sure the generalised charts would show that the 200 would carry the same weight from a shorter runway than a 300.
ps
The weight the 200 can lift (performance wise) at full noise is about 20T above the certified maximum take-off weight of the aircraft, therefore there would only be a small difference to the runway length requirement.