Black Diamond is a well-known and reliable brand. People actually summit peaks with their gear. It's backed by a great company. Skilhunt? Unknown name based in China – I'm half Chinese and am always skeptical of throwing my money down on a non-western HQ'ed product.
The Cosmo is lighter. The H03 is advertised as being lighter *without* headphones or headband. Apples-to-apples the Cosmo wins. The H03 headband also has an unnecessary strap over the head.
Cosmo – ubiquitous AAA batteries, can be found in every store. H03 – less common CR123 or 18650.
Cosmo – 200 lumen is practical for near-to-middle distances. H03 – 1000 lumen max is good for far distance and evidently they don't care about listing its adjustable output at "real use" distance. That tells me they're a marketing firm that thinks max output is the primary selling point. A 1000 lumen light is good for, say, caving but in that case I'd have a 200-300 lumen headlamp *plus* a dedicated high-output lamp.
Cosmo – red night vision mode preserves your night vision. H03 – no red. I use red *every* time I'm backpacking.
Cosmo – $22.23 to your door in 3 days on Amazon. H03 – $41 *minimum* to your door from China in who knows how long.
I've had three Black Diamond headlamps (lost my best one to my ex) and considered getting this one. I'm dumb like that. What I have works great.