In the manga's continuity, it's black. It's only in the anime's continuity that it's been shown or suggested to be a shade of brown, and even then, that's erroneous, since all Saiyans are said to have black hair only. In the anime he's been shown with brown hair.
In the officially colored manga for the saiyan and Namek sagas it's very apparently black. Vegeta's hair colour has been the subject of much discussion among fans, with some noting that it appears to change from brown to black at various points in the Dragon Ball series. In the manga, Vegeta's hair is consistently portrayed as black, while in the anime, it is mostly black but with occasional dark brown highlights.
Some fans have speculated that the brown colouration may have been a. [Dragon Ball Z] Why did Vegeta's hair change from red to black upon arriving on Earth? And then stay black wherever he went afterwards? Vegeta's hair colour has been the subject of much discussion among fans of the Dragon Ball franchise. While his hair is unquestionably black in the manga and most anime adaptations, there are some instances where it appears to be a very dark brown, almost black, colour.
Vegeta's hair, like Goku's, changes color based on his ki for various transformations. It has ranged from yellow to blue, though when not powered up it is black. Now, he has a new hair - and pupil - color for Ultra Ego.
While the regular art makes his hair appear almost all black thanks to the monochrome style, the Jump Festa art shown in multiple posts from Kami Sama Explorer suggests it's. Conclusion In conclusion, the change in Vegeta's hair color from his signature dark tone to a vivid red was not an arbitrary stylistic choice by the creators. Instead, it marked an essential stage in his character development and power progression within the Dragon Ball series.
So to answer your question: why is [King] Vegeta's hair brown/red? Unlike Vegeta's original color scheme, the King's was never corrected. The anime has always been inconsistent with colors. Vegeta was shown with red highlights and brown hair many times.
Similarly, Vegetto had brownish hair, and even keeps it in modern illustrations. Brown hair Vegeta does look kinda cool, though. I almost wish all Saiyans had slight color variation like that, it'd be more natural/realistic.
In conclusion, while Vegeta's hair appears brown in some anime adaptations, his hair colour in the officially coloured manga is consistently depicted as black. This variation in colour representation contributes to the ongoing discussion among fans about the true colour of Vegeta's hair.