The connecting record
shownDragon Ball Super (manga) · ch. 2
Beerus beat Son Goku in Dragon Ball Super (manga).
A chop to the back of the neck ends it once Goku admits Super Saiyan 3 is as high as he can go.
What each of them is ranked on
The winner · Beerus · rank 3
God of Destruction — films
His clash with Goku is depicted, and the shockwaves from it are depicted threatening the structure around them. Everything larger than that is somebody explaining: the line about being able to end a universe is Whis's, delivered as background rather than demonstrated, and the destruction of planets attributed to him mostly predates the story. His ceiling is a description; his floor is a very good fight.
shownDragon Ball Z: Battle of Gods · 2013
Fights Goku in a clash whose shockwaves endanger the surroundings.
statedDragon Ball Z: Battle of Gods · 2013
Described by Whis as capable of destroying the universe.
Beaten · Son Goku · rank 5
manga · anime · films
The longest depicted record anybody here has, and he is fifth because several of the entries above him have scored on him directly. Ultra instinct is the real thing — a state the narration describes as moving without deciding to, and which the panels back up by having him evade things he is not looking at. The screen and the page agree about him more consistently than about anyone else in this franchise.
shownDragon Ball Super (manga) · Universe Survival arc
Fights Jiren in ultra instinct in the tournament's final stage. — 2018
shownDragon Ball Z · Frieza Saga
Defeats Frieza on Namek as a Super Saiyan. — 1991
What this does not settle
One fight in one work. It is the only result the record gives between these two, and it is evidence about that meeting and nothing wider — not a general matchup, not a rematch, and not a ranking of its own.
The ladder above it is argued from everything either of them has been shown doing; this page is argued from one citation.
Where the two disagree, the disagreement is the point, and it stays visible rather than being resolved by whichever of them happens to be on this page.