If you have to choose between an Ifrit and a Nightmare, the Nightmare is significantly stronger and more effective in battle.

Significantly, you say???

In what way is it more effective and stronger???
After casting "Fear" once, the Nightmare has to run across the entire battlefield to affect someone, and it often takes more than one turn to reach them. Ifrits are flying units and permanently have a fire shield, which is more effective the more Ifrits there are in the stack. When reflecting an attack, they deal such a powerful counterattack with these shields that it's quite something.

Secondly, Ifrits are immune to fire, and therefore to any fire damage spells.

And finally, Ifrits are faster than Nightmares, both on the map and on the battlefield. :)

Therefore, I don't think it's worth talking about the SIGNIFICANT effectiveness of Nightmares compared to Ifrits! :D