The auto enhancements available in Lightroom and Photoshop fall into two categories: Algorithmic (the old way), and machine-learning powered (the new way).
Photoshop offers the algorithmic method that goes back many years. You can use three commands on the Image menu: Auto Tone, Auto Levels, and Auto Color. You can
customize how Auto Color works. But those commands are destructive, so if you want to be able to edit or remove that correction, it’s better to add a Curves or Levels adjustment layer to each image and apply Auto Color through that. Also, these algorithms can be thrown off by scans where the white point and black point were not set consistently when scanning.
Lightroom, Lightroom Classic, and Camera Raw offer the newer Auto Settings and Auto White Balance features, powered by machine learning. These tend to create a consistently better automatic enhancement than what you’d get out of Photoshop, and the results should improve as Adobe trains the machine learning model with more images.
Time is probably a consideration. The Auto Settings/Auto White Balance method should be much faster, because you can easily select a large number of images in Lightroom, Lightroom Classic, and Camera Raw, apply Auto Settings/Auto White Balance, and sit back while they process using as many cores as your computer has. The Photoshop auto corrections will be much slower, because batching will require running images through a batch action or script. This tends to be slower to start with, and processes images serially (one after the other), not in parallel like Lightroom/ACR. So Photoshop will probably not take full advantage of a computer with many processor cores.
When you consider both quality and time, the better and faster way is to use Auto Settings/Auto White Balance in Lightroom, Lightroom Classic, or Camera Raw. You’ll get both the latest machine learning technology, and parallel processing of a batch of files.
The methods above address tone and color only. They do not enhance other aspects such as detail/sharpness. To add that on in Photoshop you can add a sharpening step to the batch action. In Lightroom/Lightroom Classic/Camera Raw you could apply a sharpening preset in one step (select all images and click the preset), or use output sharpening in the Export (Lightroom Classic) or Save (ACR) dialog box.