Which "Image Editor" and "Page/Object Editor" Programs Besides Photoshop and Illustrator are compatible with Acrobat X?

Inkscape works. That's the only freebie art tool I have on my work box, but I would imagine anything else that can open the relevant content will work just as well.

I've never used this feature before but even though I have FrameMaker configured to use JPG compression for images, Acrobat keeps sending the assets to my editing program of choice as PDFs so I guess you're limited to apps that can open those (on a whim I tried Visio, no go). Since you have to manually change the app in the preferences menu every time you want to try a new one, I would err in favor of a more all-in-one solution like GIMP. Or, you know, Photoshop.

Inkscape is likely one of the very few that works with this Adobe Acrobat feature. I earlier tried many other applications to include GIMP without success. Like Inkscape, GIMP presents an import from pdf window when the Edit Image function is activated from Acrobat. However, GIMP is not integrated as well as Inkscape is with Acrobat. The GIMP changes are discarded and not reflected in Acrobat when GIMP is closed but the Inkscape changes are saved in the PDF in Acrobat when Inkscape is closed..

I'm sorry to hear more stuff didn't work. I wonder if GIMP could be made to work better with some manner of output plugin to better support PDF printing?

At least Inkscape is OK. Gimp is a middling Photoshop clone, but I think inkscape is actually marginally better than Illustrator.