Heroes 5.5 WarGame Edition - Tactical Edition.

A Phoenix with initiative 6, damage 120, and HP 510 will be much stronger than a Phoenix with initiative 13, damage 48, and HP 150.

It depends on the goals, of course, but in general, I would argue... As I said, initiative=6 is very low for a summon; yes, 120 damage is great, but I'm afraid that by that time, the battle will already be decided without the Phoenix. With initiative 13, you have many more tactical options: to finish off someone, to eliminate ranged units, etc.

Also, consider the 100% damage reflection fire shield; a larger Phoenix will leave much more burn damage behind than a smaller one.

This is relevant up to a certain point. Otherwise, it will be like in the joke about cowboys.
--Ouch, what just flew by?
--It was the Elusive Joe...
--Really, the Elusive Joe?
--I don't know... But who needs him anyway?

The peak of the active form, with maximum damage per unit of time, occurs at spell power 12 - this is a Phoenix with initiative 9, damage 90, and HP 360.

Well, this is already relevant. But isn't that too much of a limitation? Spell power 12... If this is the hero's primary stat, which grows faster than others, it will be a bit sad... Although the comment about elementals is also logical.