Photoshop is definitely superior, it handles colours better, it is quicker and the experience of using it is smoother.
Gimp on the other hand is free and that should not be taken lightly, Photoshop is currently affordable for most people on a payment plan but it is still quite expensive and the software is locked down to a limited number of computers.
Gimp is great because of its portability and it is powerful enough to use in most situations. I use Gimp when it is either impossible or inconvenient to use Photoshop.
Photoshop handles layers better than Gimp, at the time of writing this article you still can't select multiple layers at a time with Gimp. Layers in graphics programs are like sheets of tracing paper laid over each other to create a final image. You can edit, scale and move each layer as you like in both photoshop and Gimp.
Gimp is great software and is very extendible, it is also very quick inside the linux operating system (linux is sort of like mac os X except most versions of it is free). Photoshop does not run smoothly in linux, you need windows emulation software to get it working properly. Gimp was originally designed to run in Linux so it is a great experience to use it in its native environment.
Where Gimp really shines over photoshop is its image interpolation capabilities (interpolation is scaling images but not giving a blocky effect).
Photoshop mainly uses Bicubic interpolation, although it is very quick and reasonable quality Gimp gives you the choice between several types of mathematical formulas.
Gimps Image interpolation choices.
Photoshop CS6 interpolations choices
Gimp can open photoshop images but don't expect them to look exactly the same, Gimp just doesn't have all of photoshops features.
Photoshop also goes into areas that gimp barely touches, for example 3D and animation. One of the biggest areas photoshop wins over Gimp is with layer styles. Layer styles are specialised filters that you can put on a layer to create bevels, glows shadows, etc.. they can look very realistic. you can get a plugin that allows you to have layer styles with Gimp but the experience is better in photoshop because it is quicker and more customisable.
Both Photoshop and Gimp are large programs and they both take a while to learn and get used to. Overall photoshop is more professional software, if you have a choice I always think the industry standard (Photoshop) is worth investing time into learning. But as mentioned earlier gimp's biggest advantage is it is freely available and of course free to use.
To show how much potential gimp has I have included an entertaining video showing off Gimps capabilities.