Going from Small Country to Moon level is a huge increase, so they undoubtedly got vastly stronger. I do agree that with their current training regimes, they wouldn't make as major increases though.
It's one year later than it'd normally happen (ie. Age 762), not one year after the 23rd TB as I assume you read it as.
In this case, almost everything goes the same. I don't see Goku and Piccolo powering up that much from a year since they seemed to have hit their earthly limits after the 23rd Budokai. Vegeta and Nappa arrive one year later and Freeza knows about the Dragon Balls through them.
Now, there are two options:
A) Goku dies of the heart virus in Yardrat
In this situation, the Earth gets destroyed by Freeza and King Cold. Boo's ball is found roaming in space by Babidi and Boo eventually gets revived and consumes the universe unless Beerus or Zeno do their jobs.
B) Goku gets cured of the heart virus
Here things basically become a "what if Goku never got the heart virus?". Once the twins appear Goku suggests the Rosat and the twins get effortlessly destroyed. Babidi gets thwarted since Vegeta got to settle things with Goku and they both probably achieved SSJ2. Beerus doesn't threaten to destroy the Earth but it doesn't even matter because
he's not canon SSJG will be unlocked anyway. Boo's absence won't even be a bother since Kaioshin will probably take Boo's indestructible egg to protect it himself and it will only take a small fraction of Goku or Vegeta's power to hatch it.