The primary difference is that Homelander was not born with his powers - he was created by the use of injecting the fetus with Compound V until their powers developed.
Due to this, the Vought Superheroes don't have "Weaknesses", like Superman and Kryptonite. And Homelander is at the pinnacle of the Vought American heroes. His powers are:
- Superhuman Strength
- Invulnerability
- Superhuman Speed
- X-Ray Vision (with the exception of objects/surfaces lined with zinc)
- Heat Vision
- Superhuman Hearing
- Flight
Source
The comic series also mentions longevity, similar to Captain America, but this is not mentioned in the show.
However, the theme of "The Boys" is that (most) superheroes are actually not the "good guys". They are more corrupt than most supervillains in any other series, because they are only "acting" like the good guys. They are in fact megalomaniacs, narcissists, or mentally twisted in one way or another. They do have "weaknesses", but only in the way that there are holes in their "defenses". Queen Maeve is severely depressed, A-Train is a drug addict, and Translucent is a deviant, as well as only being bulletproof on the outside.
Homelander, on the other hand, appears to only be fearful of Stillwell; the only thing that keeps him under control.
However, this only lasts so long once he realises the truth about his creation, killing her and the series ending with him meeting his son - the offspring of one of his crimes.
However, if the comics are anything to go by (though certain events in the TV show have already diverted from this) as mentioned before, Homelander's mental state is his ultimate downfall
In private, Homelander shows signs of approaching a mental breakdown, talking to his own reflection in a mirror and having bouts of nausea.