I've used both pretty extensively, and like both of them for different things.
Invoke
- great in/outpainting interface
- iteration workflow is superior - that is, if you hit Invoke multiple times without accepting a generation; with auto, every time you hit generate it resets the image viewer
- infinite undo is great
- masking is better, since you can zoom in via the interface; in auto, I have to use the browser zoom to get really granular, and if I'm using my trackpad it's possible to accidentally hit back and lose everything
- has a great gallery function that lets you quickly save and come back to generations; with auto you pretty much have to manually manage your generations (the plugins to do so didn't work for me, personally)
- checkpoint caching works great
AUTOMATIC1111
- Dreambooth training built right in
- checkpoint merging
- extensions and scripts extend the functionality and let you choose how things function; Invoke basically just has a few ways to do things, and no way to mess with them much directly (there's one Hires fix type thing, but it's not usable on the infinite canvas; in auto, you have multiple options)
- flexible and powerful upscaling
- works with SD2 and safetensors
- has an in/outpainting extension that shows promise (though I'm not sure it's quite there)
- prompting is superior
So, yeah, bottom line, Invoke is kinda my "I want to make a complicated masterpiece and don't need to use really complicated prompts" while AUTO is the default for everything else. AUTO's built-in in/outpainting is serviceable, but the workflow isn't nearly as fast. Maybe in the long run an AUTO extension will surpass Invoke. Or maybe I'll try that Photoshop AUTO plugin again - that showed promise, but was pretty limited