I have been able to watch the first two episodes now as well.
The story is basically the same. Slightly more condensed at this point due to it being planned for 26 episodes rather than 39 (the original was planned for 39 and cut to 26 during production due to ratings....kind of like Star Trek).
The production staff says that after the second film things will be different. Already it looks like they are taking some ideas from the manga and cutting out some of the sillier or illogical elements of the story. The ship looks like an old battleship because they were using that as a cover to fool the Gamilons into not paying it any mind (under what looks like the wreck of Yamato). To cover the bottom of the ship, they now have missile tubes. Plus a higher chance of three dimentional combat were the ship pitches and rolls to bring the guns to bear.
The crew seems less generic. Everyone had a position prior to Yamato. Either Naval or Army Forces it seems. The uniforms have much more detail (ranks, units patches, and other things). The male to female population seems to be roughly 7 to 3 (three women for every seven men). And while the Army Women wear skirts, the Naval Women wear pants just like the men.
They even have included some things for what would have been the laters series..."Captain Gideon" (Hijikata) has a final talk with "Captain Avatar" (Okita) about going in Okita's place. Hijikata would have gone due to Okita's injuries, but Okita insists on finishing this mission. They have known each othe rlong enough that Kijikata knows he can't change his friend's mind. It is a touch like that that makes the future relationship between Hijikata and Yamato's crew feel more special. There were hints of it orignally, but this makes it better.