I've had Skylum Luminar software for a couple years, but use it sparingly. I have my workflow in Lightroom and Photoshop. Last week I had some Milky Way shots that I processed in LR, and I was happy with them, but decided to invest a little time in Luminar to see what I could get.
My original edits in LR/PS highlighted more of the magenta and orange tones. In Luminar I deliberately shifted to more blue and yellow.
When I edited in LR, I also used Photoshop more that usual. For me, PS is primarily used for cloning or removal of objects. For these shots I did a lot more layers and masks to bring out the detail in the foreground. I typically had a saturated layer with colors I wanted, a desaturated layer that I overlayed in PH, and a layer exposed for the foreground that I masked into the the sky layers.
In Luminar, I was able to do all the layering with the program. The only need for Photoshop was to remove a sign that was distracting.
My rough Luminar workflow starts similar to the LR workflow, but the first layer (sky magenta/orange) turns the saturation down just a bit. Then I add an image layer where I adjust the sky color for blue and green. I couldn't get overlay to work the way I wanted, so I used the opacity slider to blend the layers. Next I used one or more image/adjustment layers to edit the foreground. Once those layers were edited, I merged the layers and ran the denoise tool.
I like the results I got with Luminar. I'm not sure if it was the software, or just deliberately working toward a different result.