Why does Bahamut cost more to summon than Leviathan?

Leviathan does ~5000 damage to each enemy (39 MP). Bahamut does ~3000 damage to each enemy (66 MP).

Does Bahamut have any effects, aside from damage, that would justify the higher MP cost?

In actuality, Leviathan should do less damage to most enemies. According to a mechanics FAQ, Leviathan's Big Wave attack (or however it's localized in your version) has an attack power of 195, while Bahamut's Mega Flare has an attack power of 250.

However, what the real root of the MP cost difference, besides the attack difference, is that Leviathan's attack is Water element, which means it will do variable damage based on whether the target resists or is weak to the element. Meanwhile, Bahamut is non-elemental - it's guaranteed to always be doing about the same amount of damage no matter who you're attacking. This reliability and essentially undefendable nature is what causes Bahamut to cost so much more than Leviathan. I can guess that the extra damage you're getting out of Leviathan is probably because of hitting an elemental weakness.

Bahamut is non-elemental, meaning he will very consistently deal damage. And in some games he deals unblockable damage with no regards to magic defence, but I can't seem to find whether that's the case in FFV.

Basically Bahamut is valuable because he is consistent and can be used in situations where an enemy resists or blocks water/other elemental damage. I can't recall specific situations where he's ideal though other than Necrophobe(ia), it's been a while since I played (and I rarely used summoners).