The major similarity, at least in the minds of some, is that both systems treat the countries of the "South" in essentially unequal ways. Both of them use the South as a source of things like raw material and cheap labor. Both sell finished goods to the South, keeping it at a disadvantage.
The major difference is that the relationship is not necessarily fixed in today's globalized world. The rise of the "BRICs" could not have happened under colonialism. India would have been permanently subordinated to Britain under colonialism whereas now it can in some ways compete with American companies. China has risen to the point where it might actually be considered part of the "North."