Well, I guess we'll start at the beginning, with the Spanish.

The Spanish probably expanded the most 'organically' out of the colonial powers. By which I mean, Spanish expansion most closely resembled the same kind of expansion we would see in the old world. The Spanish colonial empire was based entirely off of their conquest of the well-developed areas in Mesoamerica and the Incan Empire. As such, they were unique in the fact that social structures already existed in the conquered lands. Contrary to popular belief, the Spanish didn't really change that too much. Native nobles were allowed to remain noble houses and continued to hold positions of relative influence. What then developed was totally unique, there was a resurgence in a political system that had been missing, presumed dead, for the best part of a century by 1492. Feudalism!

Yes, native and castillian noble alike were given plots of land, and became responsible for the labourers on the land, and the land itself. The Spanish crown then took some of the profits of these noble landowners. It's an odd system, and very much unique to Spain. It was also woefully inefficient. Feudalism is pretty crap as a tool for organising large empires, as the rest of Europe worked out around the mid 1300s, and eventually the inefficiency would reach the point where the empires costs outweighed its benefits and Spain collapsed, economically, around the late 17th century, and then militarily, around 1714.

Second in the colonial rush were Portugal. Now, Brazil is very different to mesoamerica, there were no existing social structures, no cities, no huge expansive plains for city planning and development. What was there was a whole tonne of resources, which the cash hungry Portuguese empire were very much interested in. The Portuguese system thus relied on squeezing as much cash from the Brazillian coast as humanly possible. Millions of slaves were shipped from Africa to chop brazilwood and farm cash crops, all to make the elite of Lisbon filthy rich. Portugals entire empire was built around this system. Endless amounts of wealth would be pushed from Brazil, which would be sold across the world in trading posts from Taiwan to Lisbon to Goa, and then some of the profits would be used to buy more slaves (conditions were so brutal, to save cash, that Brazil became a death sentence for slaves, requiring a constant flow of slaves, unlike later colonies which would rely on a natural increase of breeding slaves.) It was an ugly system, but it worked for them.

France were somewhat similar in their love of money (Well, I suppose all large empires were.) but for some reason felt that all this city building and planning stuff was a bit of a drag. They also wanted the glorious word 'France' to be as big as possible on any map of the world, and so just ended up claiming vast amounts of land incredibly quickly and then not really doing much with it. They allowed the natives to live in peace, and traded with them more than most of the other powers, and only really used the land to hunt fur. Not farm, mind you, so settled french communities were few and far between. Small lodges were pretty much the only feature of most of French colonised land, apart from Quebec, and were used by small-time fur trappers. The system worked well enough, but the lack of any cities to provide any resistance ended up in the entirety of the French colonial empire being annexed by Britain in one swoop.

Last but not least, are England, and later, Britain. Apparently, the English were just naturally more adventurous than the rest of the worlds people, or alternatively, England is too damn cold, so many jumped at the oppurtunity to leave. Whatever the reason, England saw unprecedented population exchange, the 13 colonies were smaller than all of the other colonial territories, but became very urbanised and had an enormous population (relatively speaking.) So, unlike the others, England almost saw the 13 colonies as an extension of herself, with a similar administration and population. It was probably the nicest place to live, if you were a colonist. Amazingly, all this pampering was probably a terrible move for the British. It bred a large and well educated urban class which eventually became educated and large enough to demand independence, the first colony to do so. A lead that wouldn't be followed by the other colonies for another 40 years. (Or another 100, in the case of Canada, I guess the French system is the ultimate winner, eh?)

Hope this helps, even if it was a bit long!