Illustrator works with vector graphics. That means you can scale up and down your graphics within illustrator endlessly without using quality. Illustrator is mostly used for graphics that are supposed to be printed and be more 'accurate' while photoshop is more 'arty' piece of software and coming from its name - photo manipulations. Photoshop does great job with manipulation, color tweaking, etc while Illustrator does better job with texts, drawings. Thus said its more of a 'need' which one to use not a preference although its good to be able to use them both and be flexible between them.
As xypoon said it would be the best for you if you can handle both. I'm using Photoshop in 98% of my graphics related job ( mostly non printed stuff ) . Nevertheless I used Illustrator ( currently I moved on InkScape ) when I needed to make some curved lines filled with pattern ( like dotted or stroked line finished with arrow ). This is what I miss in Photoshop. Also in vector based editors you can easier imitate hand drawn pictures (rich choice of brushes that goes along spline ) - good while designing logos, icons, schemas, maps...
For vector output. Which is easy for you to resize the image you create without any resolution problem.
It's a very advanced vector graphics package that has lots of features. It's made by Adobe who always make great software and is good for the newbie through to the advanced graphics artist. I find it easy to use and it has everything a graphics artist needs really.
I have a drawing tablet and draw directly into my PC. When I would do this with photoshop, it recorded all the vibrations of my hand. (thus making it a sloppy image) Illustrator converts my strokes to nice perfect curves. Looks more professional. Also, when using Illustrator files in Flash, I can scale them up and down, skew them, etc and they are always crystal clear. (no pixelation or jagged edges) Here is a cartoon I made in Flash. The character was a multl layered illustrator file and the background was a reeeeeeeeeally big illustrator file.
Illustrator is not faster by any measure! Maybe that's because I'm not as proficient with it as I am with photoshop, but I find it somewhat annoying. However both photoshop and Illustrator should be used in conjunction for real goodies.
Actuality adobe illustrator takes some key elements of adobe photoshop to the next level and beyond. Abobe photoshop is a very popular program used by digital photographers around the world.