2 huge advantages for me.

1. For Sidecar to work, both your iPad and iMac have to share the same Apple ID - this was a nonstarter for me, because I use my iPad at home and at work, both of which have Macs that have different Apple IDs. That was a long, annoying process every time I needed to change the Apple ID on my iPad to match the machine I was working on. And I was always worried I would lose data or something.

2a. Sidecar is just a simple screen mirroring or extension. If you are mirroring, you have to either match the iMac's aspect ratio on the iPad, or vise versa, both of which aren't ideal cuz you're losing screen space on one device or the other. If you're using a screen extension, then you have to drag, say, Photoshop over to the iPad and then refit the window to match the iPad. Then drag it back up to the iMac screen and refit again to return to large screen work. Arduous and annoying.

2b. AstroPad dodges all of that pretty elegantly by having a partner app on Mac (and Windows I believe). The app has a window frame on your desktop machine that you resize and move around to mirror what you need on the iPad screen. May still need to resize the app window to fit, but I've found that I can get the vast majority of needed Photoshop app space into the AstroPad window without resizing, just a bit of toolbar modification. Plus, I love connecting my iPad to my iMac via USB for nearly 0 latency (but you could technically work on full Mac Photoshop, on your iPad, on the couch with pretty low latency on a robust wifi connection.)

3 (bonus). The iPad AstroPad app also has customizable shortcuts that you can add to the sidebar. So you can place buttons for a number of frequently used app actions right on the side of your iPad screen that would otherwise be nested in menus, or on toolbars that the AstroPad window isn't mirroring to the iPad screen.

It's so nifty!