The question of what application is best for digital painting comes up over and over again. The fact is that there is no so called "best". Which application you use is based on a variety of things. such as affordability, platform (which OS), capabilities, hardware and personal preference. Here is the run down on the ones I would suggest.
Photoshop - Though I support open-source and free software and use a lot of them when ever I can, I still can't find one that can do what Photoshop can do. Photoshop can do painting and photo-manipulation along with 3D tools that enables to import and manipulate 3D objects, sophisticated brush engine and stable workflows. It is also and industry standard with world wide support but it can be pricey and is limited to Windows and Macs. the main features that separate Photoshop from open source applications are 16 bit color, 300dpi images, CMYK support (required for some printing) and utilizes the computer's resources well. Meaning that even the large brushes respond without lag even in large files with many layers with 16bit color. Photoshop is what I compare other apps to, which is not very fair in the sense of the money behind Photoshop compared to that of the open-source community. But this isn't about fairness, but about what works and what doesn't.
Corel Painter - is the one commercial application that can compete with Photoshop. It is more for painting then anything else where as Photoshop was more of an image manipulation tool at first that morphed into a painting package and then some. Many artist have used Corel Painter along side of Photoshop.
Krita - has gone through some major changes in the last year with the release of 2.4 and has a large following. It is a far better paint package then GIMP, but has been limited to Linux until the most recent Windows build which is a "very" experimental version. I have installed on it with out any issues and seems to work well. The brushes respond well with a 3600x2400 300dpi image with minimal lag on my laptop (2.8Ghz Intel Dual Core with 8Gb Ram) but not on my desktop (4Gh 8-Core, 32Gb DDR3). Out of all the open-source programs Krita seems to be geared to professionals that need or want an open-source alternative to Photoshop. Krita is the only open-sources painting suite that supports 16bit and 32bit color, but seems that it doesn't support CMYK though the Krita web site states that it does. The one feature that Krita has going for it that the others do not (with exception of Alchemy) is the mirror tool. It is quite useful when doing fast sketches for character design or top views of vehicles. Now that there is a Windows version, I will be working with Krita more.
Usage: Professional Painting; Web Application; Concept Art, Sketching, Image Manipulation
GIMP - has finally released version 2.8 and like Krita has made quite a few improvements. But GIMP is better used to manipulate images or to tweak your paintings instead of trying to do any real detailed work. A lot of people have been wishing the GIMP would be a true alternative to Photoshop, but has not yet gotten there.
Usage: Photo Manipulation; Sketching, Images for the Web; Concept Art (8bit RGB, Tablet Support limitation )
MyPaint - is a kin to Painter and that is what is was intended to do. MyPaint has a great paint engine allowing to fine tune the brushes. The draw backs with MyPaint is the resolution is only 72dpi which isn't suitable for print that requires 300dpi normally and no manipulation tools. But the work around is to adjust your painting to be 4 times that needed for print and to use GIMP to make adjustments. Using GIMP in conjunction with MyPaint and to keep layers, you will need to use the open-raster file type (.ora).
Usage: Concept Art; Sketching; Paintings for Web Application (72dpi and 8bit RGB limitations)
Alchemy - is not intended to be a painting application but an idea starter similar to looking at clouds or shapes and finding people, faces or things within them. It is a great place to make simple idea sketches or see what you can come up with and then further detail using another application.
Usage: Sketching; Idea Starter / Experimentation
Conclusion: Even thought open source paint packages have come along way and can be used quite well to some extent, only Krita is capable of utilizing the resources of today's systems which is needed to do projects that require 16 bit color and extensive numbers of layers. Still Krita doesn't offer the tool set, layout and workflow that is available in Photoshop. But if you can not afford or don't need all that comes with Photoshop, then I would recommend the combination of Krita and GIMP as long as you are not doing more than 8bit color and you have a modern system. For lesser systems MyPaint, GIMP and Alchemy is a workable alternative. All of these open-source systems are available on both Windows or Linux.
Downloads for Windows
Krita / GIMP / MyPaint / Alchemy