It is not fair to compare these two classifications as the basis on which they are found are way different. In between these two classifications more than a century of accumulated knowledge has gone in. Just visit the following site for detailed understanding:
www.mobot.org/MOBOT/research/APweb/
Hardly any similarities, but for Monocots (a natural group as a whole, though there are major alignments within). No vertical split of Angiosperms strictly into Monocots and Dicots. You have basal angiosperms and others which are neither monocots or dicots. Please go through!
I also think it's on this page you will have the best information.
You can also download free the article "An update of the Angiosperm Phylogeny Group classification for the orders and families of flowering plants: APG III" on the site of the Botanical Journal of the Linnean Society :