Depends on what you want to do. Photoshop is good for common jobs, but if u want more detail graphics Illustrator is the best, or If you want the 3D animation graphics which is the worlds best is either Maya or 3DMAX (A ton of animated movies are made with this)
i may be a little bias only having played with illustrator for a few hours but i find that photoshop was better for what i needed to do...i could always find an exact tutorial for what i had in mind
Photoshop is hight-end software for professional designer/photographer (raster graphics). What means that objects you create are built with pixels (picture looks like blocks when you zoom it). Illustrator is great product for graphic designer and illustrator (logos, artworks, portraits - vector). Objects you create in Illustrator built with contours, so picture looks the same with any resolution. So, basically, if you want to draw - use illustrator, if you need effects - use photoshop. Both products are great and you can use each for them for graphics, but results will be different. So, if you have enough money and want to start a designer career (or just hobby), you should buy one or both of them.
Photoshop is the industry standard for web graphics etc... though there are a lot of alternatives... but it depends on what task you intend to be using it for
Photoshop is by far the best for graphic design, Illustrator is also excellent but i mainly use it for logos. Paint Shop Pro used to be alright i haven't used it in some years but it wasn't that bad of a program.
Photoshop is Standard in the graphics design industry. If you want to get into specific projects, having a nice line of other adobe applications is useful (such as illustrator for vector art).
if you want to get into the graphics industry you need to know the adobe products. they are always required in every job advert that i see!
Since i use only photoshop , so i can say that my vote will be in favor of photoshop. It is easy to use and creates very good effects.