HOB Filter or Sponge Filter
 

In the case of Dwarf Seahorses, which is better, a HOB filter sponge over the intake or an air driven sponge filter?

I think an air driven sponge filter would be better. I have the greater seahorses however and have never kept dwarfs.

I've also been looking at the old fashioned corner filters. They hold bio filter media, carbon, and mechanical filter material.

IMO, it's best without a filter. The sponge filters suck up some of the live brine nauplii leaving them trapped, dying, decaying and increasing the likelihood of bacterial problems down the road.
I use open ended airlines for water movement and live rock rubble for biological filtration, but do large frequent water changes, which for a dwarf tank are not expensive.
That being said, I DO like to use a mini filter that will collect the uneaten nauplii before adding the next batch of enriched ones. I set it up on a timer that comes on a couple hours after the initial feeding so that by the time the next feeding comes around, there are little to none of the depleted nutrition nauplii left.