What are the main points of dissent between Cyril of Alexandria and John Chrysostom? What were the main differences or points of dissent between Cyril of Alexandria and John Chrysostom? Can anyone give a summary, please?
I am by no means an expert on the subject, but I think there may be a false impression that there was a big difference between these two men. The impression is caused because Cyril was involved in deposing Chrysostom at the Synod of the Oak. However, if you read carefully, it seems that Cyril was not personally against Chrysostom, but rather that Cyril (who was overly aggressive, bordering on cruel by nature) was merely tricked by enemies of Chrysostom to think of him as an Origenists. Origenists held the heresy that all people will be saved without anyone going to hell.  The difference between the two seems only circumstantial and by personality. Cyril was ready to censure and punish heretics and Chrysostom was for a time falsely accused as one. 

When trying to read some of their works I noticed Cyril is really a very high level thinker that was seemingly brilliant with respect to understanding the trinity, so his impact seems limited to that subject.  There also seems to be less writings from Cyril extant. Chrysostom on the other hand is a less philosophical and more of a nuts-and-bolts Bible commentator. His commentary on Romans and Galatians seems close to a modern day protestant evangelical library. 

So, from my limited knowledge of these two men, I do not find any real theological differences between them. They were very different people wrapped up in very different politics. Cyril seems to have had more power in the Catholic church, but Chrysostom seems to have been more influential and charismatic upon people at large.

Chrysostom is an interesting read, especially Romans and Galatians. Some of his works can be found here.

What I found interesting about Cyril is that in arguing for the trinity he opposed Nestorius who seemed to be trying to separate the nature of the God-Man into two separate units. To oppose Nestorius, Cyril had to emphasize the unity of the God-Man and in so doing he seemed that it was necessary to over emphasis the importance of Mary, in whose womb this unity was created.  I gather that later further elevations of Mary with Catholic history actually stem as an inadvertent unhealthy spin off from Cyril's good effort in opposing Nestorius. Like an accident resulting from a victory. Of course I am looking at things through a Protestant lens.