What abilities?
Well, these specific examples don't apply to Mineserver itself, but some x86-64 builds of games can, as a result of the extra available resources, produce longer visual distances, reduce loading times, etc.
A properly coded 64bit Mineserver could have exponentially faster map generation and NPC calculation times than a 32bit server, even if both are running on the exact same hardware.
At least that is what I understand.