I recently picked up the Ice Heart Elemental core. It would, at first glance, seem to be no better than the Mental core. However, there is more to it than there seems.
First, there is the damage per item, all other Morphon cores get a +5 per item of the type, while Elemental is at +6. A minor, but notable difference. The Nuclear Powered core is similarly somewhat better than other crystal cores.
The other thing both Elemental cores give is a bonus to damage multiplier, nothing unique. The Ice Heart also adds a bonus to stun.
What actually makes it superior to the Mental core is that there is no current Morphon item, other than a core, that resists Elemental damage. That means that your average player with a Magic or Supernatural core is less likely to have an item that resists your attacks slotted.
Bear in mind, there are still Crystal items that offer considerable resistance to Elemental cores. It is just that characters who have invested heavily in Morphon items will probably prefer to have such items in those slots, a character who forgoes a morphon item in either the head or arm slot in favor of an elemental resistance item will be able to resist Elemental attacks as well as any other.