The above is kinda true, but misleading.
The issue really was whether to base the size of congressional delegations from each state on the total state population, or just on people who could vote.
The argument is not as straightforward. For example, today the size is based on population, not voters. This means citizens who live in areas with lots of non-citizens, both legal and illegal immigrants, are somewhat over-represented. There are actually lawsuits over this. The effect overall is pretty small and its generally agreed to let things slide instead of opening up several big cans of worms.
To make matters more complicated, the New England and Mid Atlantic states were just starting to abolish slavery in the 1780s, though the southern states still had larger slave populations.
As Akhil Amar shows in his Biography of the Constitution, generally the slave states got the better of the argument. Really the only thing the northern states got was to knock down the apportionment value of slaves to 3/5 instead of counting them per capita as the southern states wanted. The southern slaves states got parity in the Senate, and the President elected by the Electoral College on a state by state basis, with a bonus two electors for each state regardless of population, free or otherwise, which almost completely wiped out what would have the North's population advantage for presidential elections, if the office had been decided by direct national popular vote.
What I'm arguing is that this one wasn't even particularly close. The 3/5 thing were really the only points the North put on the board in this game.
To change this, you would have to get PODs that would produce alot of other butterflies. You could have slavery abolished everywhere in the North prior to independence, so slavery is more of a contentious issue but then you might not get all the colonies united enough to achieve independence. You could find some way to get slavery abolished in the South. Or maybe you could have the British southern campaigns be successful enough to detach Georgia and South Carolina from the US and these places remain as British colonies.