Not really. Krita and Gimp are raster authoring tools that compete with Photoshop, though all 3 support vectors. Illustrator is a vector authoring tool that Inkscape competes with.
Krita used to be a jack-of-all-trades painting program for the first few years of its existence. At some point, the devs figured out that they can get people to fund development more effectively when they focus on one usecase (digital painting w/ tablet) and make that really solid.
Ah, that's why I thought it was a competitor to Illustrator. What I use Photoshop for is photography, which sounds like it's not Krita's main use case.