Did some math versus various targets for you:
I assumed that the eliminators were past devastator doctrine, did not have any aura buffs or enemy unit debuffs, and weren't Raven Guard.
6 targets: Company Commander (T3/5+/5++), CC in Cover (T3/4+/5++), Space Marine Captain (T4/3+/4++), SMC in cover (T4/2+/4++), Artificer Armor/Stormshield Smash Captain (T4/2+/3++), and Smash Captain in cover (T4/1+/3++)
Labeled as 1A/1B, 2A/2B, 3A/3B respectively
TL/DR:
Mortis rounds beat out everything else handedly. they have AP-2 which on most characters is enough to get to their invuln save even in cover, making the ignores cover part of executioner rounds pointless. Then on top of all of that they have d3 damage and possible mortal wounds to go past invulnerable saves entirely.
maybe there would be a better choice for certain larger targets, but as far as I can tell in every possible circumstance you should never be shooting anything but mortis rounds at characters. Once all the characters are gone then hyperfrag is useful to try and squeeze some more anti-infantry shooting out of them, but again mortis rounds would be better suited for vehicles and monster hunting. executioner rounds might be better against "always in cover" units like Jormungandr Tyranid Warriors who would ignore AP-1/-2 from their adaptive physiology, so that you essentially still get a -1AP from ignoring cover in them opposed to nothing from mortis, BUT MORTIS STILL WINS FROM THE BONUS WOUNDS CAUSED.
Executioner rounds:
1A:
3 shots
2.5 hits
1.666 wounds
1.111 unsaved
1.111 damage suffered
1B:
Same
2A:
3 shots
2.5 hits
1.666 wounds
.8333 unsaved
.8333 damage
2B:
Same
3A:
3 shots
2.5 hits
1.666 wounds
.555 unsaved
.555 damage
3B:
Same
Hyperfrag rounds:
1A:
6 shots average
4 hits
2.666 wounds
1.777 unsaved
1.777 damage
1B:
Same until saves
1.333 unsaved
1.333 damage
2A:
Same until saves
.888 unsaved
.888 damage
2B:
Same until saves
.444 unsaved
.444 damage
3A:
Same until saves
.444 unsaved
.444 damage
3B:
Same until saves
.444 unsaved
.444 damage
Mortis rounds:
1A:
3 shots
2 hits
1.333 wounds
.888 unsaved
1.777 damage
+.222 mortal wound damage
1.999 total damage
1B:
Same
2A:
Same until saves
.666 unsaved
1.333 damage
+.222 mortal wound damage
1.555 total damage
2B:
Same
3A:
Same until saves
.444 unsaved
.888 damage
+.222 mortal wound damage
1 total damage
3B:
Same
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