Aseprite for anything animated. Aseprite for initial work on tilesets. I love Aseprite. Layers and animation as seperate concepts, proper indexed image support, feature packed, but easy to use.
Pyxel Edit somewhat begrudgingly for getting tile counts under 256.
8x8 tiles+not being able to copy multiple tiles at a time makes one of the primary reasons I use Pyxel Edit a bit of a hassle. (Checking tile transitions while editing one tile that links to many others.) Pyxel Edit has a select tool, but it's only useful if the place you're moving the selection to is "unmapped". And if it's unmapped, you can't edit a tile and see the change someplace else...
Pro Motion can do the tileset thing, but I find it more frustrating.
D-Pixel can also do it, but without the real time update on all tiles
as you draw.
Since, I didn't see it mentioned in this thread, Graphics Gale: https://graphicsgale.com/us/
I prefer Aseprite to it, but Graphics Gale is totally free now. Also supports layers and animation. No real time tile edit (like Pro Motion and Pyxel Edit), but really solid beyond that.
Another one I don't use but is worth a try is Nigo-CHR: https://retrodaddy.itch.io/nigo-chr
It's a bit less user friendly than NES Screen Tool, but totally does the real time tile edit stuff. It just doesn't work on my primary work computer
I've been working on my own art program and toolset as well, but I don't know if I'll release most of it. (I'd rather not focus on user friendliness and support.)