ABOUT THE PROBLEM: The problem is mathematically exact, but visually it is not as well defined. That's because the subjective colorfulness depend in a complex way on RGB hue, saturation and brightness. Photoshop's HSB system set B=the highest one of the RGB components/255, so the apparent brightness of full white is much bigger than say max bright red. Still both have B=100%. In addition saturation doesn't be the same as the subjective colorfulness. That quantity is called chroma.
Let's check the math side (= how to averagely match saturation and brightness). HSB separation with HSB/HSL filter obviously gives something to you. After applying it to a RGB image you have hue in R channel, saturation in G channel and brightness in B channel. After the separation you can adjust saturation and brightness curves. You can check the average by applying Blur > Average and undoing. Finally filter back from HSB to RGB.
Photoshop hasn't blur adjustment layers for fast exact processing, but you can use smart filters instead.
Here's our test images as layers. They have same hues, but the top layer is too bright. It has also too much saturation. Both layers are converted to smart objects.
This is our stack for the equalization:
Both layers have got HSB separation filters and averaging blur filters. There's a single layer mode curves layer. Its G channel is used for saturation equalization and B channel for brightness equalization. The too bright layer has blending mode difference and the goal is to make G and B channels both black in the channels panel. It can be checked best with the color picker, because black and dark grey can seem too same.
After adjustment we remove all filtering from layer Wanted. From layer "Too bright" we remove averaging and group that layer with our curves layer. The blending mode is changed back to Normal.
The group is converted to smart object and it has got filtering HSB to RGB. If the curves are adjusted ok, the result should be = the wanted.
We can check with blending mode Difference how close we got it:
It looks perfect, but there's still a percent of brightness left. I guess it is caused by lousy adjustment without the color picker.
You can rasterize the result to get a normal image layer.
The success so easily is based on a non-realistic thing: The goal needed both brightness and saturation reduction. With practical images which need increasing there can occur clipping and the result still isn't numerically right.
The visual side:
CIELAB color system (=Photoshop's Lab) would be theoretically better than RGB when you want different hues which should look as bright and colorful and want to get it with numerical adjustments.
Unfortunately in CIELAB you can far too easily drift out of the color range which can be shown in RGB screens. In addition Photoshop doesn't have the polar form HCL (Hue, Chroma, Lightness) of the Lab color mode nor a handy way to separate H, C and L. Thus the Lab subject isn't digged deeper in this answer.
Be practical: I guess that without some special software you must do it visually because numerical adjustment as shown doesn't present properly the subjective appearance. Have several textures opened in separate windows at the same time and use adjustment layers to be able to tweak the colors iteratively. I guess having only 2 visible at the same time isn't productive.
Flatten the images when you are ready.