I finished Clannad and Clannad: After Story quite awhile ago and wrote up this review shortly after finishing After Story but never posted it. (It has probably been sitting for at least four years while I tried to decide whether to finish and post it.) While both were good, I sped through Clannad in large chunks-- not the fastest I've run through anime, but it drew me on. After Story on the other hand took me nearly twice as long to complete.
The original Clannad had, as Kyou mentions of Okazaki in the second season, a "cynical" sort of humor blended with drama in a refreshing fashion. In the second season, the humor within the story dropped precipitously-- which I wasn't expecting. After Story certainly evokes a great deal of emotion, however, much of it consists of dealing with the anxieties and disappointments of modern life. For the reasons I used to preface this review, that focus reduced my enjoyment of the second part.
Clannad: After Story is consistently rated as better than the original series, likely due to the evocative storytelling and deep storyline. And it is an excellent series. However, as I was discussing it with a friend, we both felt that the heartwarming moments seemed to be placed into the series almost with the sole point of making the drop afterwards that more heart wrenching.
That has its place, but for me, it wasn't something that I was looking for when I began the series and I almost literally had to force myself to finish.
If you're looking for a successor to the original Clannad, I'm of the opinion that you're better off looking elsewhere. After Story is an entirely different sort of story that explores themes and emotions with a heavy hand that had a light touch in Clannad. It is a story that is told well, but it isn't what I was hoping for from a sequel.
If you watch the series, watch it for itself-- it is not light entertainment and I'm of the opinion that the genres listed for the series should also include tragedy. The goal behind a tragedy is to engender catharsis and After Story will likely do that for you if it is something that you need-- if you don't, it isn't likely to leave you happy.
