Always go to a fitter. That being said, I've skied both the Hammer 130 and the Hawx Ultra 130, I've worked on both as a fitter.
From a fitting standpoint:
Both have a heat moldable shell, the Head allows for about 3-4mm of adjustment with the shell mold while the Ultra does closer to 6mm+. Basically, if you've already got a low volume foot you're good either way. If not the Hawx is a lil easier to make work, Hawx also holds a punch better. Hawx has a higher instep, especially over the lower foot. In comparison the Head being a three piece accommodates nearly any instep but does sit a little lower over the top of the ball of the foot. This is the one area that the heat mold doesn't really help with. That being said a heat moldable three piece is huge and you can accommodate a lot with that alone. (i've got like a 102mm last and I fit just fine)
How they ski:
Head is way more progressive, as any three piece boot is. Also they ski way damper (this may be a lil different in the 130 but i'm sure it's similar), they eat up a lot of vibration more so than my kryptons and definitely more than any two piece overlap boot I've ridden. Which means they hammer off piste and through shit chop and crud, especially with a huge ole ski. They also fuckin rail, lateral stiffness is way better than the krypton or any other three piece boot I've ever used. This is likely due to Head riveting the tongue in place rather than dalblello/full tilts method of allowing the tongue to move back and forth. They also absorb a lot of shock when you send shit to the parking lot and land flat. TLDR my favorite three piece boot to date. Which is funny cause I hate head boots (usually) race shit is bull shit (usually)
Hawx is very progressive for a two piece overlap, laterally a lot more stiff. Carves better, better edge control, still rails everywhere. Forward lean adjust is nice, I ski them upright and love them. They definitely excel over the head on piste but only just. Hawx is about as good a two piece as you can get, also they are light as shit which is nice. The hawx is one of the most responsive boots I've skied that actually fits and isn't some race stock shit. Huge performance, comfortable, lightweight. The forward lean adjust, volume adjust, and flex adjust are huge too. Let's you really dial it where you want it.
Basically if you prefer a wider or longer ski, stiffer skis, like to charge off piste, or like the really progressive flex a three piece gives you for butters or really flexin through into spins etc. then go Head. If you prefer superior edge control, carving fast and hard, want something light and don't really give as much of a shit about super progressive flex as long as it fits and gives you the power you need go Hawx.
Hope that helps