I don't know about the specific metal makeup used by each, but the obvious difference between the Eliminator and Hunter and the Easy series is the cutter profile. The Easy uses a flat top profile and does scraping and not cutting. While the holder may be able to accommodate a different cutter, is may not have the tip clearance to use a cutter tip with the same profile as the Hunter and Easy.
The other issue is will the screw that fits into the insert work with an insert from a different manufacturer? In my limited research to create a carbide tool over the last year using off the shelf inserts, I have found that the Hunters and Eliminators of the trade have inserts unique to their tool. Meaning (at least Hunter) the manufacturer has done a lot of work to ensure that their cutter seats perfectly with their "set screw" (I use that term loosely, but the screw that holds the insert onto the tool).
Carbide inserts for woodturning are somewhat unique to woodturning. Yes, there are some similarities to metal turning apps, but what I have found is they tweak the carbide manufacturers dies to afford them a level of performance you can't get with an off the shelf insert. You can buy inserts for less that will work, but I don't think they work as well as the ones from a Hunter or Eliminator (I don't own an Eliminator, but have a lot of Hunter tools).
Pay the money, use the insert that the manufacturer sells.