A short-haul flight does not spend much time in its cruise level (let's say less than two hours). Thus, it is important to rapidly reach the optimal flight level and I think this kind of aircraft should be optimised to climb. On the opposite, on long-haul flights there the climb and descent reprsent a tiny portion of the whole flight. The aircraft should then be optimised to consume as little fuel as possible during cruise, even if climb rate is less important. That's why I wonder if my thinking is right and if there are significant differences in climb rate between short and long-haul aircraft.
Related thinking: On average, does a short-haul flight descent more rapidly than a long-haul? I think not as this diving has no reason to be related to climb/cruise performance and all commercial aircraft are made to use the same airports with the same approach pattern; but that's only an assumption.
EDIT: OK, the quantity of fuel is quite important. I suppose an aircraft designed to be heavier (long-haul, carrying lots of fuel and payload) is equipped with more powerful engines and thus if it is lighter than designed for (lets say a B777 or a A330 used on short-haul flights), it climbs faster than the same aircraft in a long-haul flight. But the long-haul aircraft is designed to make long-haul flights. Maybe I should have asked if there is a significant difference in climb rate between short and long-haul aircraft at their maximum operating take-off weight.