If you want to balance Juggernauts across ELOs, buff anything except their damage
Almost all recent buffs to relevant juggernaut champions has been to damage. I'd like to demonstrate why this is a terrible idea and why Riot should buff underperforming juggernaut in any way except for damage.
From recent memory, you can see:
given +20 more AD on his passive at max rank (translating to higher damage across all abilities), higher AD scaling and a lower cooldown on W, higher armor pen on E.
Ult: Total health regenerated increased to 50 / 75 / 100% of maximum health from 40 / 50 / 60%. Subsequent patches nerfed his E's AD steroid by 20-30 at max rank based on missing HP.
Q damage increased by up to 40 at max rank. Later nerfed by 20. Armor/MR passive from W increased by 10. W given 60% tenacity in the first .75 seconds. E given % armor shred on targets hit by 4 spins.
(upcoming) E cooldown reduced by rank 1, unaffected at max rank. Ult cooldown reduced by up to 20 seconds at max rank.
Lifesteal increased by 2/3/4% per rank of passive. E armor reduction changed from flat to percentage. R now halves his Q cooldown when activated.
W attack speed increased by 15% at all ranks. E scales better with AD, R's steroid scales with AD.
can cast other spells while Purge is active. No longer rooted while grinding someone in his R. Q delay reduced from 0.85 to 0.6. Passive cooldown reduced from 30-10 to 30-2.5 (though no longer effected by CDR). R missile speed increased to 3200.
Noticing a trend? The buffs that have had the most significant impact are the ones that dramatically impact usability or defense. While most Juggernauts have been sadly relegated Bronze-Gold pubstompery as a result of Riot's poor balance, some of them have been lucky enough to still make waves all the way up the ladder. Garen is now a viable champion all the way up to Masters (though preseason hasn't been friendly to him); Urgot is an A+ if not S tier champion across every rank; Dr. Mundo briefly terrorized everyone as a strong response to season 8's short-lived mage meta when Riot attempted their diversity plan in bot lane.
On the other hand, the raw number buffs that are doled out to the champions in terms of strictly damage have had little real effect in the long term and do not solve any of their issues keeping them from seeing high ELO play; those issues being that they are far too reliant on one form of defense (sustain) to survive as well as not being able to reliably reach a viable target compared to how easy they are to lock down and burst. Garen's Q getting a damage buff has only further stigmatized him in lower ranks despite his W buffs being far more significant in reality. Nasus gets continuous buffs mostly to his ability to output damage and yet can never stay meta longer than a month, even when the game should favor him. Darius has only become more of a pubstomper than ever, while continuing to have middling performance in higher ranks as the game accelerates past him. The Olaf changes, simply put, didn't do anything; they didn't even shake Olaf off of his full tank builds like Riot wanted him to. I suspect the Illaoi changes will have the same effect; the E cooldown change is most relevant against players who have poor positioning that will actually enable E to be used off cooldown to begin with. The R change, while nice, still does not address her intended design as an anti-engage champion vs how laughably easy it is to stunlock her on an engage and kill her before she can do anything.
If you want to give Juggernauts meaningful changes that don't make the lower ELOs hate them even more vocally than they already do. Then you should improve their usability, target access and/or their ability to defend themselves. Handing out flat damage boosts to them does not help them in higher ranks where they can rarely actually apply it, but makes them incredibly overbearing in lower ranks. Hell, you could even nerf some of their damage if you want to give them more ambitious survivability buffs, and I'd call that a good deal almost every single time.
not have a 2 minute cooldown on a shitty heal over time would be a nice start