Preface: While writing this out it turns out we're both ignoring a lot of variables, time included. Rather than mess of text this, here's the TLDR/W.

Black mage wins assuming ever increasing mob density that dies after 60 seconds or within 10 seconds.
Summoner wins assuming mob packs of 3-6 that die between 20 and 55 seconds.

PS: Guess which one is more applicable.
PPS: This is then not a matter of who got out better, but who is currently better suited for current content. In terms of AoE: Summoners are better suited for current content. Black Mage for when things need to die right god damn now.

I still want my flare back.