Staggering Vana at the right times can interrupt his spawn animation, which is especially useful on P5. Spamming it can make it possible to go a full fight without him spawning anything at all. The problem is that you'd have to rely on move-and-shoot weapons, like alchemers (inc. charges) as with a Blitz unload time, even stunned, Vana'd still probably spin far enough around in time to at least cause you to worry. Shiver mitigates the problem entirely. Other than spawn interruption, there's really little reason to use Stagger over Shiver as Shiver is simply safer and more guaranteed, and can also freeze up the Slags in P5.

As for LD, it's the other way around. Half the populace wears Skolver so is immune to Shiver, then you'll have any number of others who happen to have freeze resistances, so short of hanging onto Shiver for opportune moments, you won't often get a chance to actually use it. Stagger however, is useful as it slows people down by a serious amount, even when strikers boost. With slow weapons they become more vulnerable than dangerous, although you do need to watch out that their damage will still be the same, even though you just won't be able to believe it, watching how slow they move. Worth it though. Although, as Pipinn said, there're more options than just Stagger. VT is the commonly used haze as it works on most people and at the very least scares them off. VT and Stagger work a treat, mind you; perfect for killing!