Blue Elemental Blast and Hydroblast are two very similar pauper legal anti-red counterspells.

Why might one prefer one over the other?

The same question applies the red counterparts Red Elemental Blast and Pyroblast just as well.

Namely Hydroblast can target even non-red spells and creatures. It just does nothing. I can see that this might be beneficial in decks where you want spells cast for other reasons. Or maybe fill up your graveyard.

But then is there any downside to running Hydroblast? Is it just strictly (if marginally) better?

I don't know of any downside to running Hydroblast instead of Blue Elemental Blast, it is technically strictly better.

It costs one or two bucks more I guess ^^ ?

Not being able to target = illegal target if you were stupid enough to target invalid thing, say devoid.

Which matters in a way that opponent can't force you to go forward with your bad decision, you just roll back the state.

Hah yeah I have done that exact blunder. Those pesky Chrysali... I suppose it might indeed matter in games of sufficient stakes.