Well I did notice the old "space knots" from the original as a measure of speed has been changed to the more ambiguous "S-knots". They also mention "Cosmo Speed" as another unit of velocity, which I don't remember from before. I really like how the Gamilas have different names for our planets. Their names elude me, but they refer to Jupiter (Kubilli, I think) and Saturn differently than us, which makes total sense. Why would they use human names for worlds?
The wave engine and wave motion gun are all the same and Okita actually has an internal debate with himself over the gun's use - their primary mission being the preservation of earth and not of the complete destruction of Gamilas. The power of the gun really gave everyone pause when they wiped out the floating continent, since they were only aiming for the Gamilas base at its center.
The first warp scene is really good, and I liked the pilots playing darts during the warp. It's one of those things that I always liked about DS9 and NuBSG - predominantly Ron Moore's writing style, as well as Joss Whedon with Firefly and SHIELD, showing seemingly innocuous and generally unnecessary scenes of everyday life below decks with lesser characters to add flavor to the overall story quality. And I'm enjoying the initial tension between Kodai and Yuki. The whole story is brilliantly written so far.
I am amused at the Japanese use of an American trope, however. In the scene on Pluto where they find Kodai's brother's crashed ship, the Gamilas send robot people to go after the humans. IIRC, the American version of the original occasionally changed Gamilon soldiers into robots (or maybe it was the tank drivers from the Comet Empire - can't remember) so they didn't have our heroes killing other living beings every week, while the original Japanese had them as real people. In this version, we actually do see robots being used as soldiers controlled remotely.