I LOVE the analogy: it really got your point across perfectly.TheDevilsCorpse wrote:I personally think you are taking the rivalry thing a bit to literal. Goku and Vegeta are like polar opposites in terms of personality, the only thing they share is a love for battle. If you combine those two together you get a stronger individual in terms of a person, not power. From the little bit we see him in the manga, Vegetto lacks character defects which in turn makes him closer to the perfect ideal of man. The only trait that we can see as bad for him is his being cocky, but a lot of that seems just to be based on his trying to get Buu to absorb him, a way to enrage his opponent. As for the actual power of the Potara fusion is still just Goku x Vegeta, though with everything balanced out, would have great potential for improvement.
Goku fusing with Gohan on the other hand would present a stronger fighter, but in general, the resulting character would be almost the exact same as Goku or Gohan individually. They share very similar personality traits, though the new fusion may enjoy battle a little less and possibly pick up a book on occasion. The resulting character would still have much more power than Vegetto to start off, but all the similarities would prevent growth the same way.
Think of it like this, Vegetto is a 100 piece puzzle and the Gohan/Goku fusion is a 1000 piece puzzle, though Vegetto ended up with less pieces all of his fit together while the other character's box got all the same pieces twice, so you can never finish it correctly.
I see it as both, though. Not some "rivalry = magically produced more power when they fuse", though, so much as their rivalry resulting in two very different fighting and ki gathering styles being created. Being both in one, Vegetto can combine both styles to create a new, significantly more powerful style. In the very few instances when that's not possible, he can simply choose to use whichever is the more efficient.
So if Vegeta had 9,000 power and a skill X that lets him use up to 3,000 power in one technique, while Goku had 10,000 power and a skill Y that lets him use 5,000 power in one technique, Vegetto would have a power of 19,000 and a skill XY that lets him use 8,000 (or more) power in one technique. Meanwhile Gohan has a power of 15,000 and skill Y, so his fusion with Goku would be that "Gokan" has a power of 25,000, but can still only use 5,000 power in one technique.
From another perspective, Goku and Gohan both know how to make the same tomato sauces. Their fusion would result in someone who knows how to make tomato sauce too, but not "more" or "better" tomato sauces. As a cooking rival to Goku, Vegeta knows how to bake bread products instead of also learning how to make tomato sauces. His fusion with Goku gets us Vegetto, who not only knows how to make tomato sauces, but also how to bake bread products. On top of that, having intimate knowledge of both, Vegetto knows which sauce to add to which in order to make pizza. At the "Saiyan Cooking Fair," Goku always scores a 2.5/5 for his sauces, while Vegeta scores a 2/5 for his breads. Vegetto's pizza scores 5/5, which is higher than both Goku and Vegeta's scores combined.
It's the same concept in regards to rivalry affecting power; the higher Vegetto's skill, the higher his overall fighting strength will be.