Well, having experience with both, lets see here....
1. Springs are just that. They are one piece, generally shorter than stock, where you just replace the OEM ones and reinstall the whole thing back into your car. Very inexpensive ($150 to $200 for a good set) Some swap out the new springs and run the OEM strut, which is ok depending on your drop. Anything more than 1" and I recommend performance struts as well.
Pro: cheap, easy, many manufacturers available
Con: not adjustable, have to redo everything to change ride height (i.e. when selling the car)
2. Add-on Coilovers (i.e. Skunk2, Ground Control, etc.) These are replacement items, much like the springs mentioned above. The consist of a shorter spring as well as an adjustable sleeve that goes over the strut (OEM or replacement). These cost more than the springs alone ($250 - $350 per set)They usually allow for adjustment between .5-.75 in. drop (all the way up) to 3-3.5 in. drop (all the way down). Do not use these with your OEM struts, the ride sucks and your struts will go to hell within a few thousand miles.
Pro: Adjustability, cheaper than full coilovers
Con: Not as effective as full coilovers, rough ride
3. Full Coilover (i.e. TEIN SS). These I feel are the best in coilovers. These are the fully adjustable spring AND performance strut in one piece. Much like those above, they are adjustable from .5 to 3.5 in. drops. Usually, the stiffness of the strut is also adjustable. You can really fine tune your ride and handling characteristics then. But, keep in mind, these are more expensive. ($1k or more)
Pro: Highest quality, full adjustability
Con: Cost, few manufacturers available.
Lastly, someone mentioned about camber, with springs, once its set and camber doesn't change. With coilver, your suspension and ride changes as the car is raised and lowered. Camber set for when the car is at .5 in drop is going to be different than when the car is at a 3.5 in drop, because all the rest of your suspension components are at different angles to the struts depending on where it sits. I have my car's camber and alignment set for 1 in drop for daily driving, but dump it for shows. Conversely, it looks good for shows, but I have to raise it up to drive around, or else my ride sucks and my tires will suffer for it.
Well, hope that helps you and your buddy!