The K5 is a heavy breacher, the edge is thick, so it's not for delicate work, wood chopping, and it's probably too heavy to be a fighting hawk. I'm sure it's well made, there's a good video review on You Tube, it's easy to find.
The GG&G Battlehawk is just as thick as the K5, both are 3/8" thick, throughout, they aren't tapered like a Winkler. The GG&G has a thicker edge angle than the K5, it is not going to chop wood, but it will break it, eventually. The 44oz weight is pretty massive, considering it's only 13" long. One negative, as a breacher, is the large opening behind the edge. It can get hung up on the inside of a car door, or house door etc.. and slow you down. You will need to wear gloves with this one, the G-10 is pretty textured, and has a sharp edge all around, it's tore up the palm of my glove, but it's grippy.
OTOH, it's indestructible, the DVD they sent with it shows them using it to wench a Toyota Landcruiser, the GG&G has a chain aroundthe handle and it's placed between some rocks. The 44oz weight causes lots of damage, it will force itself through sheet metal, break chunks off of fence posts, and the spike is very serious. I've thrown this one over and over, I'd hurt myself before I could hurt it.
I didn't plan it this way, but by owning the GG&G it has helped my endurance towards my other hawks. It's the same length as the Winkler-Sayoc, but it's 20oz heavier. So, after training with the GG&G, the Winkler feels very fast, to me.
It's not for everyone, nor would I grab it for backpacking, camping, fighting, bushcraft, throwing, or anything other than breaching. And then, I'd only carry it in a vehicle, not on my person.
One last item to mention, the sheath is great, it's a Buy Brown, the website doesn't mention that, but mine came with it.
I've never held one of the LaGana's, but out of the three you mentioned, it would be the fastest in hand, for fighting.
You should also look at the Self-Reliance tools/Omnivore tools
http://selfrelianceessentials.com/category/tomahawks/