Is there? The damage difference is negligible and the root is the same duration.
Do mobs have increased resistance to lower ranked Frost Nova?
Is rank 1 Frost Nova the only rank I really need?
Everything I’ve ever heard, during Classic and back in original vanilla, is that no, you have no reason beyond rank 1.
But I want to put this comment in here in case I was wrong.
That’s what I’ve heard/read as well
There is literally no reason to ever train Frost Nova past rank 1, as the snare effect is applied the same and breaks the same across all ranks.
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It is 50 damage for 90 mana. In perspective arcane explosion 5 vs 6 is 62 damage for 75 mana. Difference being nova is more escape/shatter. AE is dps, for multiple targets.
It is not that much damage but it’s also not that much mana. Frost crits likely do double(spec), improving the ratio. Both eat a clear cast.
Personally, I would consider a macro that casts one or the other based on which you care about at the moment. Make the default cast r1, the shift cast r4.
If they lose a pvp encounter in which the enemy has under 50 hp and they have over 90 mana left - i guess there was a reason to use it 
Test it is all I can say.
Yeah. The way I see it is if the idea is you are so strapped for mana that 90 is going to make a difference, 50 damage may make the difference too. Happens both ways sometimes you oom, sometimes you don’t do enough dmg fast enough. Thats why a macro that does both is the best way.
One spot would be when you recall in AV.