The Dutch get better prices. They also get a better ship at the beginning. As Colonization is all about the economy, the Dutch are perhaps the best. As hard numbers are not available about the difference in prices from other powers, it's difficult to tell if they're really all that much better and if so by how much.
The English get more immigration. It's very useful in the early game, but immigration will be a relatively insignificant way of getting colonists later. You will get more immigrants on the docks than other powers, so get Brewster as soon as possible (as the first father if you can, even before Minuit), or you'll be getting all the useless criminals.
The French have better relations with the natives. They also get a Hardy Pioneer. The Hardy Pioneer is useful, but not as much as the Dutch Merchantman. If you start in a place heavily populated by the Indians, better relations will spare you many problems.
The Spanish have a bonus for attacks against the natives. They get a Veteran Soldier. They're the weakest power if you use the typical strategy of early peaceful coexistence with the Indians (unless, of course, you want to deny that advantage to your opponents). To exploit their benefits start an early all-out war against the Indians, and get Cortes as soon as possible for extracting huge treasures from their cities, then get Brebeuf and Sepulveda for converts. Washington would be great, but you can get him only after 1600.
Import some horses for your Veterans, equip immigrant Criminals/Servants with Muskets and possibly also Horses, buy a unit or two of Artillery. Use all the money you get from Indians for raising more armies (but don't buy Veteran Soldiers; they're insanely expensive) and getting new colonists. Make Converts work in the field (in the early game you won't have many experts, and they work as well as Free Colonists in farming/planting jobs; get Casas in the middle game when your population is already about half-expert and Converts' skills cease to be that useful). Plan wars as campaigns that end with one of:
- destroying all villages of one Indian tribe
- destroying all villages of one Indian tribe on one island (of course don't leave them on an island where you have colonies)
- destroying a few villages and then their capital
This way you won't be attacked by them when your armies are elsewhere. Because you have many more armies, use them against other Europeans early on. The Spanish require a different strategy, but aren't necessarily weaker than other powers. Try keeping the Indians you fight away from your colonies. If they ambush armies in the field you lose some Horses or Muskets, or maybe an Artillery is damaged (but why would you leave it unprotected?). By attacking a colony they can destroy buildings, kill colonists etc.