You don't see the problem? Goku and Vegeta are not rivals in terms of power
Only with Goku at SSJ3. In base, SSJ, SSJ2 they are rivals and considering they fused in base then mentioning a rivalry over that works just fine.
b. They're both competing each other aka ''outdo each other''.
I repeat: Goku is aiming to be the strongest, he lives to be the strongest,
not to outdo Vegeta. Outdoing Vegeta was only a part of it when Vegeta had strength beyond Goku's (Saiyan saga). Right after it, Goku barely looks at Vegeta like someone he has to surpass, some hit mark. They CAN be rivals because they are seeking the same general goal (be the stronger), but so would be Vegeta and Piccolo at the at Freeza and Cell saga, considering it's stated Piccolo also aims to be the strongest. Therefore, the "they live to outdo each other" is highly innacurate as "outdoing each other" is just a byproduct of wanting to be tue strongest. Still relying in VIZ?
Option a. has its flow, both are not rivals in terms of power.
They are in the form they fused (aka base). Just because Old Kai didn't mention "they are also rivals, well, except Goku has SSJ3, which Vegeta has not", which is just silly. If they are rivals in base, then the point old Kaioshin might be trying to get accross works just fine, as they fused IN BASE and being close to each other might help in making the Potara even stronger.
Why shouldn't SSjin3 be included?
Because they fused in base and comparing each other's base would be enough to reach the conclusion of "they are rival in power and it helped the fusion". Mentioning SSJ3 would be irrelevant as they performed the fusion in a state they are both on par with each other... done!
The fusion can still work but that wouldn't make them perfect since they're not rivals like Goku and Vegeta. Unless you think Goku and Gohan will received a rival boost too if Goku suppress his power to Gohans.
If they are somewhat close in power, then sure. Goku doesn't have to suppress in order to fuse with Vegeta, while he would have to suppress down when fusing with Gohan, and there lies the difference. Kaioshin and Kibito, for example, weren't close in power, yet they suddenly fused through the Potara. IMO, Kibitoshin sucks because Kaioshin and Kibito were "weak" and also pretty distant in power. We know Kaioshin is much stronger than base Goku/Vegeta and yet Kibitoshin is way weaker than their base... yet a fusion between them does seem to be way weaker than even base Vegetto... whereas you can believe that they got a boost due to wanting to "outstrip each other", I prefer the explanation that, since they were already ~ the same in power, their fusion would just be much better.
I didn't deny that, the rival boost comes with extreme rivalry like Goku and Vegeta had unlike their kids playful rivalry which is laughable at best. What's more
Now you are just making it out to be Vegetto's boost would be bigger because Goku and Vegeta 's rivalry would be greater, whereas even the rivalry's definition doesn't entirely support this.