My thing with alicorns is, firstly, theres only 4 known so far. They're "goddesses" in the show, and have the ability to raise the sun 'n moon so on and so forth. Thats just it. They're not meant to be like other ponies.
As for unicorns, their powers to me seem limited. I think of it like this. Unicorns are like mages, if they want to actually have that much power, they have to study and practice. An example from the show is that Twilight took ages to learn how to teleport a significant distance.
Pegasi are my favorite. They can control the weather and fly, but take flutter shy for example, unless they actually train they aren't getting anywhere quickly.
Last but, oh lets face it, least, the Earth ponies. Not hating of earth ponies but they are underpowered. In the show however, they are depicted as a hardy race, capable of anything they put their mind to.
So yea thats my break down on the "races" of ponies.