Raster VS Vector

Raster images
Also referred to as a bitmap graphic, a raster graphic is the most common kind of image found on computers. Raster images are made up of a grid of pixels, each pixel is assigned a colour value, and with enough pixels a computer can create the illusion of a crisp image. If you were to enlarge one of these images, you would lose the sharpness and quality of the image as the pixels became more clear. Depending on the height of the resolution of a raster file a picture can look incredibly crisp. An extreme example of this would be this 320 Gigapixel panorma photograph of London. Which allows you to see extreme details from huge distances. The problem with this is that the pixels in raster images require a large amount of disk space, so creating pictures like this is not easy.
Raster files come in formats such as .BMO, .TIF, .GIF or .JPG. Raster images are often created and edited in software such as microsoft paint, or adobe photoshop.

Vector images
Unlike raster graphics a vector graphic is not made up of a grid of pixels. A vector image is very good for media printing because it's size can be increased hugely without any loss of image quality, this is because vector graphics use geometrical formulas to represent an image. Instead of being made up of a grid of pixels, they are made of shapes called "objects". You can edit each objects shape, size, position and colour Common files formats for raster are .CGM .SVG .ODG .EPS .XML. Vector files require very little memory to store them Vector graphics are often edited in software such as Adobe Illustrator, Adobe Freehand, Pro/DESKTOP.
Before vector graphics can be translated into the physical world from a computer through a raster based output device such as a laser printer or dot-matrix printer, the vector image must be translated to a bitmap to create. A limitation of vector graphics is that they cannot handle phtographic images as well as a raster format can. Because of this, the best time to use vector images is when creating large scale illustrations and logos.

Raster Or Vector?
There is no better graphics format. Both raster ad vector graphics can produce brilliant results simply by understanding the strangths and weaknesses of both of them. Where one fails the other one will likely compensate in that area.