Vegeta's GREATEST Rival was NEVER Goku... It's Trunks
In Dragon Ball Z the Super Saiyan Prince Vegeta NEVER had a rivalry with Kakarot. Future Trunks was the MOTIVATION for Vegeta to train hard and ascend to the next level. This is Ascended BS btw. Check this out.
Thumbnail - BrusselTheSaiyan
Source - Screen Rant