Heavy improvements to the mecha are one draw. Massive space battles were a draw before, but improving on it makes it rather impressive. The Battle of Pluto was exciting in the new version. While the original also had feeling to it, it was not exciting as a battle. Yamato's weapons are similar to how they were before, but the effects make them appear even more impressive. Add to this what was shown in the Chapter 4 preview of the Gamilas Fleet vs. the Comet Empire Fleets, and you get what is basically mecha fanservice. Glorious mecha fanservice.
The deeper story for the Gamilas is another. Before they were kind of generic enemies that were not quite evil, but you generally didn't care what happened to them. (At least not until the second season when we started to care about Dessler). Now they have families, dreams, goals, and personalities the audiance can relate too. One can actually feel sorry for Schultz and his men. We didn't feel sorry for them in the original. They were the bumbling underlings originally. Now they are just unlucky to have to face Yamato first without any real knowledge about it. They were clever, but just not prepared to deal with something like that. Dessler comes off as a good leader from the start. Some of his generals seem alright. Dommel gets to show off his tactical leadership in battle the first time we see him. We are waiting to see how they do the Galman Wulf sub commander, who was one of the cooler characters of the Yamato III series.
Adding more women helps as well as there was always the complaint of Yuki being the only woman on a ship full of men and doing pretty much every non-combat job on the ships, from food planning, to away mission specialist, to radar operator, to nurse, to ship's activities planner, and laundry. She did practically every job on that ship at least once. Now they've spread some of her larger tasks up (radar operator, analysis, nurse, fighter pilot (live action film)).
While the Nurse (Makoto) certainly has fanservice appeal, it seems to be Yamamoto that is getting the most attention after Yuki. Yuria and Niimi seem to be getting stories as well in the next two Chapters, with Makoto still being mostly just the nurse that cares about how others feel.
The story this time around is faster paced and things seems to have moved on faster while still telling the same amount of story, while adding even more to it. That would sound impossible until you think that the original was sort of slow paced for the first half of the series with several redundant episodes that basically told a similar tale a second time, or there was a lot of narration about the story so far, or the place they were going (some of which is now quite wrong since space exporation has come a long ways since 1974). With a lot of that either cut out, or the explainations handed over to the characters, the pacing is faster with less redundancy.
Since episode 7, the story has drifted farther away from the original stories. They were about the same for the first six episodes, with some differences, but seven was were things really started to change. Sure they are still going to the same place for the same reason, but how they go about it and what happens along the way are changing. You might find a new episode's plot to be similar to one of the older plots, but things are becoming more and more different. We have had one story that is nothing like any previous plot, and one that is only marginally similar to two or three other plots while being a completely different story (using an element of an other story with an element of another story, and then making a new plot that has those elements within it).
Take episode 10 for example: There are elements of three stories from before in there.
A. A captured Gamilon pilot (first time humans have seen the Gamilas in person).
B. Trapped in a Space Graveyard
C. Trapped in a region of space with one Gamilas ship that shows them the way out (though that was not on purpose in the original)
These elements are combined and altered so that only the elements are similar to the original series. You have Yamato get trapped in a weird dimentional pocket that is a ship's graveyard, with one Gamilas ship that can help them escape. To foster confidence with the humans, a lone pilot is sent to do face to face meeting (first human contact with a Gamilas citizen). Those are the use of those elements, but the story is not like any of the three episodes those elements were from originally.
So it is the same...but also very different. And it works.