In general terms, laser printers have higher resolution so they have better print quality. Inkjets create images by spitting out tiny droplets of ink, so their resolution is lower. If you look closely at a page printed on a laser printer and the same page printed on an inkjet, you will be able to see that the laser has smoother edges to the fonts.
Inkjets are the way to go (as of 2003) for cheap colour printing. Some of the more recent inkjets provide exellent colour clarity and brightness, and are very well suited for printing photocographs. Also, inkjets are usually quite a bit cheaper than lasers, and colour inkjets are MUCH cheaper than colour laser printers.
While inkjet printers themselves are cheaper, their ink is much more expensive. Ink cartridges need to be replaced fairly often if you print alot, and especailly if you're printing pictures, and ink cartidges are not cheap. On the other hand, toner for laser printers is pricey, but will rarely need to be changed. If you're using a laser at home, you may never need to change the toner.
All in all, each printer has its function. Inkjets are great for limited home use and for photo printing. Lasers are good for high-volume applications, live offices, or for applications that need extremely high print quality.