The capacity of the case relative to the size of the bore makes quite a difference. For example, the 243 Win. and 358 Win. are both based on the same 308 Win. case, but they need different powders.
To go a step further with it...the volume behind the bullet changes as the bullet moves down the bore, and the larger the diameter of the bore and bullet, the faster the volume behind the bullet increases. In that case the powder needs to be transforming to a gas at a faster clip to maintain pressure (which is needed to get the velocity we love so much), so we use a faster burning powder.
Conversely, with a smaller diameter bore and bullet, we don't want the powder to burn too quickly. The bullet's movement provides pressure relief and if the powder is generating gas too quickly for the acceleration of the bullet to relieve pressure, bad things happen.
