In an interview with executive producer Brad Wright, he said:
"There is new material, but most of the new material is visual effects or scenes that have been cut. It is tighter. It is significantly tighter. ... The editing pattern is different, and therefore the performances are different. It's a different movie."
I haven't found a definitive list of changes but from further reading (for example, the section regarding the Goa'uld Tel'tak on Wikipedia's list of starships in Stargate article, which indicates that the Tel'tek was first introduced in the season 3 episode Deadman Switch but later added to the final cut of Children of the Gods) I am under the impression that maybe Brad was playing down some of the changes a bit?
What are the differences in the remastered Children of the Gods?