Spey, which works better for processing wood for a fire?
That answer lies in the hands of the user, and how they choose to "process wood".
Example Considerations:
1) The thicker geometry of that Norse Hawk (photos above) wedges wood more effectively, while the geometry of that Frontier Hawk bites deeper. So, if for example a user likes/chooses to split wood standing on a chopping block the thicker geometry is gonna pop the rounds better with less stick (where I go, never have a chopping block so negates this potential benefit).
2) Same exact principal when cross-cutting, the thicker geometry is gonna pop chunks sideways to a greater degree clearing a bucking V. Easily compensated for by simply initiating a smaller V initially, then expanding.
3) One works better with a baton than the other.
4) One is heavier than the other (better for some things, not for others).
5) Each has strong & weak points when using head removed from haft. Example: pole-less Frontier-Hawk fits comfortably in palm of hand Ulu-style for various push-cutting tasks feather-sticking, etc., whilst the extended pole on a Pipe-Hawk or Trail-Hawk make a nice striking surface for a baton when held as a chisel in hammer grip.
I started daily carrying a hawk on my pack ten plus years ago. Initially began with the Pipe Hawk because it seemed to make sense to have a hammer-pole (obviously makes a good hammer, chisel, and also to balance the energy of the bit in relation to the haft when assembled), but it was not long after I found a Frontier Hawk suited my uses much better. I find the lighter weight (increased acceleration/speed), taller bit (edge length), marginally shorter bit (center of haft to edge), and minimized pole to be advantageous combination to my uses. I would have simply cut the pole off a Pipe-Hawk, except for when you actually compare the other aspects of the two.
A friend of mine prefers the Trail Hawk. However, it is commonplace for him to be disappointed with the performance when using for fire-building, and choose to leave behind for other options. Example: The short edge length really leaves this hawk wanting when it comes to actual work performance I.M.O. (many more strikes required bucking & chopping). Those sexy looks are an energy whore in my experience.
Off the shelf they all kinda suck ..., compared to one that has been optimized for the users specific applications (haft coating removal & treatment, reprofile edge, handle length adjustment, head to haft fitment including loosing that stupid Allen set screw, sheath, etc.). Without these modifications, performance & user appreciation is sure to be left wanting.
Repeat:
"I would suggest buying (or getting into hand ...) any/all of the models that interest you, and making your own observations as there are many differences that many folks ignore, overlook, have no use for, etc."
This would give you multiple handles (replacements for potential breakage, varied handle length options 16"-22"), and heads to compare based on your applications.
"Better" ... ; is best accomplished via the hand of the tool using the tool, than the tool itself.
EDIT: if all you want to do is "processing wood for a fire"
I would look at the Rifleman's-Hawk (beast heavy for a hawk) or Hudson Bay Hawk, and also consider picking up a longer 30" haft from a Viking Hand or Battle Axe.