It seems slow, buggy and has been a disappointment to those of us who have come to expect better. We use Macs because they 'just work', and Catalina doesn't.
There's a few bodge fixes available, which i've gathered here.
General slowness
With thanks to Twitter user @SarikaidenMusic here's one solution:
"Boot up the mac while pressing & holding Command+R until it boots into recovery options, then select Disc Utility, and then run First Aid. I did it to all my drives to be safe, but you probably only need to do it to the one macOS is installed on."
I also did it to every drive. It's made it better, although not as fast as it used to be. My Mac is a few years old so i don't expect top performance, but the change is speed is noticeable.
Many users reported lagging and general slowness making the user experience painful.
Apple Music memory leak
This one is particularly bad. It might only effect people with music collections in the thousands, based on what I've read, but Apple Music started using up more and more memory until the system crashes. Ands this repeats.
The workaround seems to be:
Go into preferences -> advanced and untick automatically update artwork
Go to your music folder - > iTunes and delete the Album Arrtwork folder
Restart.
Now Apple Music should be using between 200-600MB, which is much more sensible.
Photos
It's slow to start with but just let it run it's course - it's just scanning all the photos to give you new collections