The show contends for my favorite TV anime of all time, for sure. Back in when S1 was first airing on Toonami Mike Toole ran a Big O forum on animejump and we actually used up all his bandwidth multiple times because we posted so much about each week's episode. I think that was the best anime community I've ever participated in, and the main reason for that was just because the writing in the show was so strong. Big O is awesome for its style, atmosphere, music, fucking rad giant robots that exemplify what giant robots should be, etc, but I think its strongest suit is its characters. The relationship between Roger and Dorothy is perfect and timeless, and they have some of the best dialogue I've heard in any TV show, anime or otherwise. It was really subtle and mature and funny, and it holds up very well now. Probably Chiaki Konaka's best work.
S2 still has a lot of great moments, but it is sort of a shame that the show had to end with the "lead actor negotiates with the producer to continue the story" thing, as someone aptly pointed out. It's painfully obvious that the creators wanted another season. And so did the fans. But everything has to end eventually, I guess.
I think S1 had a better ending, and when I think of the show I like to remember that great moment.