Warning: contains ENDING SPOILERS for Invincible and The Boys!
Two superheroes of nebulous moral character have skyrocketed in popularity in 2021: Invincible's Omni-Man and The Boys' Homelander. Both are clearly based on Superman and both are secretly violent, ruthless killers with their own hidden agendas. In their own worlds, few can stand a chance against them in battle, which begs the question; what if they battled each other? Judging from their own fights and histories, a definitive answer presents itself, and the results might be surprising.
Both Invincible and The Boys have concluded their comic series (Invincible ending in 2018 and The Boys ending in 2012), and since both Homelander and Omni-Man die at the end of their stories, it is a demonstrable fact that neither man is immortal and both can be killed. Moreover, both have similar power sets: Homelander and Omni-Man possess flight, super speed, super strength, and invulnerability to most conventional weapons. Both are also not above killing their enemies, sometimes brutally so, to get what they want. But that's where the similarities end.
Homelander was the product of Nazi genetic engineering and chemical experimentation though his publicists paint him as an alien who arrived on Earth and adopted all-American values, a la Superman. Homelander has many powers that Omni-Man does not, and most of them give him a decidedly long-range advantage. His screams can rupture eardrums, his X-ray vision can see through any material with astounding accuracy, and he can hear heartbeats from a distance. His heat vision in particular is perhaps his most deadly power; he's sliced a plane clean in two, tore through dozens of people, and even incinerated his entire medical staff during his birth. In the end, the only being capable of defeating him was himself, in the form of his own clone (the secret identity of Black Noir), who was created as a failsafe in case the already-unhinged Homelander ever decided to rebel against the company that created him. Where bombs, missiles, and other superheroes failed, Black Noir succeeded, and Homelander was brutally murdered by his own doppelganger.
Indeed, Homelander is uncontested and unchallenged through most of The Boys...which is (unfortunately for him) one of the many reasons why Omni-Man would soundly defeat him. Unlike Homelander and his manufactured backstory, Nolan Grayson actually does hail from another planet. Specifically, Omni-Man is a Viltrumite from Viltrum, a race of impossibly strong beings who live for thousands of years, if not more. In part because of his lifespan, Omni-Man sees the people of Earth as lesser beings and has absolutely no reservations about killing them by the thousands.
Unlike Homelander, Omni-Man has fought other extraterrestrial beings of comparable strength. He's fought for literal centuries, and while he may not possess heat vision or super-hearing, he has the considerable experience to negate those advantages. He single-handedly murdered the Guardians of the Globe (the Invincible universe's equivalent of the Justice League) and even massacred an entire planet's worth of aliens completely unopposed. Nolan can accomplish this feat because his Viltrumite physiology allows him to travel through space (by holding his breath for weeks). In a similar fashion to Homelander, it took another Viltrumite to finally defeat Omni-Man for good - fellow Viltrumite Thragg eventually killed Omni-Man after a long battle.
To put it mildly, things don't look good for Homelander in a one-on-one fight. Though Homelander may be the most powerful superhuman on Earth in The Boys, his lack of any real challengers might also be his biggest weakness. Omni-Man's sheer durability combined with his centuries of experience in battle makes for a considerable uphill battle for anyone foolish enough to challenge him, even a fellow evil-Superman-style "flying brick" hero.