Goku became at least 800-1000 times stronger with godly ki IN BASE, because:
---Enraged Vegeta >>> SSj3 Goku. Let's say that DBS SSj3 Goku is stronger than Ultimate Gohan and SSj3 Gotenks, which is ridiculous but whatever. The gap between them should be tiny, because Vegeta was extremely impressed and scared that someone was able to take Gohan and Gotenks down that easily, just like he did with Goku. Beerus one-shotted Ultimate Gohan and finger-flickered SSj3 Goku. But Enraged Vegeta was able to TANK an attack from that Beerus, so he should be far, far above Goku, Gotenks and Gohan.
---That Vegeta was still unable to sense godly ki, even though he was much, much above the 3 guys mentioned above.
---Whis implies that you have to wield a certain amount of power while having godly ki to be able to sense godly ki.
---Krillin stated that Goku was much stronger than whatever he had been before.
---As we all know, the SSj3 multiplier is base x400.
Therefore;
Base Goku Post God >>> Enraged SSj2 Vegeta >>> SSj3 Goku
This easily implies a 800 or 1000x gap, perhaps even higher.