Photoshop - GNU Image Manipulation Program
Illustrator - Inkscape
Office - Libre Office
All are as-good, if not better.
Not better is correct.
Gimp is the best free photo editor, but people who think it's just as good as Photoshop don't really know what Photoshop can do. Gimp doesn't have CMYK Color mode, or Pantone color, or spot color, which is critical for something commercially printed. It can't handle Camera Raw files, which contain hundreds times more information than jpg and other files Gimp can read. While Gimp can open PSD files, the chances of it being rendered properly is about 5 percent. Non-destructive edits with complicated composites is impossible with Gimp. Gimp has a single healing tool for pixel Manipulation, and it's quite limited, whereas Photoshop has 4 such tools with infinite fine tuning with each. Gimp is perfectly fine for simple image editing, I've used it a lot, but for something more sophisticated or detailed, the more powerful tools of Photoshop win out.
Inkscape is actually pretty good, especially if all you need it for is digital art, like websites, icons, app GUIs, etc. It's great. But it lacks that CMYK color output and, like Gimp, Pantone color matching.
Libre Office is actually pretty good. It will do most things that most people want to do in an office suite. It kills MS Office in file compatibility, as it will open pretty much anything, and can even save files in ebook formats. Sometimes documents render weird in Libre Office, because it can't properly use MS fonts. I tend to stay away from the MS font alternatives and go with Helvetica over Arial, for example. Solves that problem.
The downside is, the people who code and review the system are not user-focused, rather they are developers who are tool-focused. So by nature it's clunky, bloated and a little crash heavy. Having said that, it's a top notch alternative to MS Office, and the way Microsoft is headed with their online-only, always-connected model, making standalone, offline productivity more difficult (not yet, but that's where they are headed), Libre Office becomes an even more attractive option.