The plot for this is pretty much the same as Batman the animated series, in that there really isn't one. Like with BTAS, the show primarily follows Clark Kent/ Superman in a series of episode driven plots. There's no real overarching story to it, and like with BTAS, I think it works for this kind of show.
What helps with this are the characters. I do have to admit that I've only recently gotten into Superman, so its not my place to compare these interpretations to all versions of them. However I can compare them to Man of Steel's ones, and these triumph over them because the feel like characters the whole time. Before I get hate for it, I'm not saying that the characters in Man of Steel aren't characters, its just that they feel like exposition machines for large chunks at a time in the movie. The sign of good writing, when exposition feels like characters having a conversation, not feeling like exposition.
The animation is on par with animation at the times, which is still very good, but in comparison to some, has nothing going for it. When comparing it to BTAS though, the art style is a lot brighter. With Gotham, you always see it at night, or near night time. The world is full of darker colours, fitting in with the Batman mythos. Here though, there's a much larger focus on day. The world is brighter, blue skies a lot of the time. Excuse the bad joke, but the differences in animation really is like night and day. Even the music shows how different the two shows are, with Batman is was more brooding, unless the character called for it, like Joker, but with Superman, its again more colourful, joyful to an extent.
What pains me about this is that I couldn't give it more time, because it is very good, from what I have seen, especially if what many say is true, and you need to wash the sour taste of Dawn of Justice out of your mouth. However, the cheerfulness is not to last here, because we return to Gotham, and we go to the future, with Batman Beyond next week.