Well, my favourite drama so far is Honey & Clover. If this is something near then it's going to be good. Though I must say that I'm not too much into (anime) drama. If this is not about a bunch of girls falling in love with a boy for no reason then I'm OK.
If you both like drama try Orange. It's still on air but, what I've seen so far, is pretty good.
Well, Clannad is basically about 3 saga. The first is about a little (but just as old as the main characters) girl and the mystery around the weird things that surround her. The second is about an extremely smart and talented, but shy girl, and unveiling her secret past and trying her to be the part of the group. The third saga is when the love plot which is hinted throughout all previous two saga, though it remains in the background, but this time it gets the main stage. Don't worry, they won't go over the top with love drama, there is not actual drama involved, like having numerous girl interests or so. Also, if you hate the "I love you! Please, don't love me back!"-type of storytelling, I suggest you skip the OVAs.
Anyway, it's not as bad as it sounds, basically there's a group of friends who solve all these mysteries while goofing around, and eventually crying a lot. The most heart-breaking is probably the first saga, I'm already tearing up just by thinking about the final scenes of it, but the third one is the most important in terms of After Story.
Now, After Story is also about sagas. One of them is a highly spiritual one, which will explain some things later on, but overall, it did not leave a strong mark on me. It's average. The second one is much more interesting, and I think it also involves the main characters as side characters, but I like the climax of that saga, that is pretty powerful. But the main reason After Story is regarded so highly is because of the second part of the season, when it's about the (by now, because the group is separated by work and such) two main characters. And this is why it's important to watch Clannad. To use a not spoilery example: the main male character, Tomoya has a best friend, Sunohara, and during Clannad they are at each other's throat all the time, but they love each other. They are going through a bunch of silly stuff together, like, Sunohara is beaten by girls every two episodes or so. Childish things, but by After Story, the contrast of real life just makes these memories all the bitter. They can barely even meet, they are both trying to make a living in their shitty jobs. It's like everything and everyone withered away. They share extremely few screen time together, but obviously, those are rather powerful, and those who saw the anime, know the exact scene I would link here now (football pitch).
Also, there is an overarching storyline that begins in Clannad, and takes place in an unknown place and time. There is a little girl in a room, all alone, and talks about strange things. She doesn't know how she is, why is she there, or if there are anyone else there besides her. Needless to say, it's a cool part of the story, but progresses extremely slow.