Summoner has superior single target damage, a black mage wont beat it nor come close to it.
Assuming both are equally skilled players that know their class to perfection.

The black mage will destroy the summoner in AOE damge, not because summoner is bad, but because black mage is pure burst damage that doesnt stop, while summoner has to set up their cooldowns/dots, spread them, and they can only hit up to 3 targets with bane, so they have to switch to another undoted enemy and reaplly + bane again.

Just that factor will make blm come on top on instances where AoE damage is dominant. yet on same instances against a boss, you will see the summoner winning the race over the black mage, i have seen the differences to be about 20 to 30% in some cases with two equally geared casters and knowledgable players.