In addition to what Rex said, PixInsight is specifically designed for processing astro images while Photoshop is a general purpose image processing package.
Photoshop is very powerful and learning it has value for all sorts of image processing. It's OK at astro images. In the right hands it can do a fantastic job. It's not incredibly easy to use but there are lots of books and other resources that will help you with the basics.
PixInsight has a lot of very powerful tools for processing astro images. Some of these are unavailable in Photoshop or are additional packages that you need to buy (e.g. gradient removal). It's challenging to learn if you're not a computer/image processing geek but not impossible. There are no books but there are some free videos (Harry's Astroshed) and some you can purchase (IP4AP.) It's of limited use for non astro images. It's not free but it's cheaper than Photoshop.
Hope that gives you some idea of the trade offs. I'm a keen PixInsight user but I've tried not to be biased
Cheers,
Rick.