Vegeta would have much less problems with what would be considered an elite saiyan surpassing him, even if he is a half-breed.

Goku on the other hand was born lowest of the low-class (ironically, even though Bardock was a badass), born with a PL of around 2, that somehow surpassed the prince of all saiyans with enough training (something the Frieza Force as a whole didn’t believe was very effective), that was a way bigger blow to Vegeta’s pride.

considering that Prince Vegeta broke every record in saiyan history when he was born…

And probably had his father preach that to him for quite a while when he was a kid.

While taking care not to ever mention a very peculiar saiyan brat he banished that had actually far surpassed even Prince Vegeta the fourth’s latent battle power.