Kaioken is not a form. It's a technique that increases power x2, x10, x100 etc. Goku used this in base form to defeat Vegeta for the first time. He was only able to do this again with SSB because of SSB's superb ki control. He'll toast if he uses this in other SS forms.
The SSG (red) was attained by Goku when he was lent power by 5 other saiyans in his fight with Beerus. Since Goku attained SSB, there was "no" benefit to use SSG since it's only around 10% of SSB.
In the manga, Vegeta achieved SSG (defense, movement) and effortlessly shift to SSB (attack) to overwhelm Goku Black. In the anime, Goku is shown to shift from SSG to SSB but not as subtle as Vegeta in the manga. My hunch is while Goku will have a new transformation giving him power edge, Vegeta will be shown to have mastered this, giving him the stamina edge.