I'll be crucified for saying this, but I'll say it anyway.
There's no need to watch the first season to comprehend or like the second season. If you're not up to excessive moeness and a dull story, the prequel might end up making you don't watch the sequel, which would definitely be a waste.
You can get a pretty good idea of what the first season was by watching the first 8 episodes of Clannad ~after story~. All the mistakes from the previous series are there. Lame humor, dull drama, unlikely reactions to over-dramatized conflicts and a weak soundtrack.
I was very close to dropping this anime thanks to KyoAni stupidity in copying every single aspect from the prequel. There were some improvements, it's true. After episode 8, the soundtrack was much better and even the art seemed more beautiful. Also, I have to admit that, thanks to being 4 episodes long (contrasted to 7, 8 episodes long arcs in Clannad), it wasn't that hard to watch Sunohara's and Misae's arcs.
Thankfully, some light shone upon Kyoto Animation and they realized that a more tangible plot without relying in nonsense supernatural references or in bad jokes every two minutes would work way better to actually create a dramatic environment.
From episodes 9 to episode 21 we are delivered a beautiful and extremely saddening story of the hardships of becoming an adult, having dreams, seeing they fall apart and getting over dark times.
Hardly did an anime approach these topics in such an effective way without losing focus that they are dealing with human beings and not perfect beings who are flawless or solve everything with some tears and "I'm sorry" all the time (which basically summarizes the first installment).
Tomoya's adult life's story unfolds in a carefully detailed account of how life can be a bitch. It's really easy to connect with him, suffer with him and cry with him many times, too. It was a wonderful development to his personality making him an extremely likable character, probably one of my favorite male characters ever.
Nagisa had some development, too. But overall, I still felt a bit annoyed by her quite often childish personality. Even when she acted a bit more independent and adult-like it was hard to not think of her as a child.
Ushio goes without saying. Probably the main reason many tears were shed in this series. Her voice actress did a wonderful job in giving life to such a special child.
But in the end KyoAni couldn't resist revisiting old mistakes. In the very ending it was decided, in a way that seemed completely out of the blue, that after causing so many tears, telling such a beautiful, tangible and human-like story they would laugh hard at your face and say "Just kidding, it was all a lie".
It was completely uncalled for. It fell like a rock, crushing everything that had been done up to that point. I understand the need of a happy ending. But one thing is ending happily, another thing is destroying 13 episodes of development just for the sake of an unreal conclusion.
I was more disappointed from this outrageous flaw than I was from watching the first series. The feeling I got was "Oh, we didn't have the guts to make the story follow the pace it was following so far, so we decided to change everything in the last episode just not to make you sad anymore. Here, have some candies"
Once again, a poor ending causes tremendous damage in a very promising show. It always angers me the desperate need of a complete surreal "happy" ending that so many movies, animes, series, etc have rather than showing a more soothing and human-like ending.
Still, it's a highly enjoyable show. Just don't expect much of the conclusion.