Since I saw the play 24 times I figure I should probably stick my head into this conversation.
First of all, let me say, that if I saw the movie first I would probably be asking a similar question. I love the movie but it cannot even compare to how good the play was. In my opinion the primary reason to watch the movie is because I can't watch the play anymore and I want to see those amazing performances over and over again. To have the film as a way of preserving the performances given by those actors is something I am very thankful to have.
Second, I found (and some people are sure to disagree with me) that the ending of the movie is not as fulfilling as the end of the play, in regards to Posner. I'm not going to go into the differences between the play and the movie here in detail because I recently did explain most of them in another thread you could search for if you'd like.
Moving on, the chemistry between the boys on the stage was so vibrant you could feel it no matter where you were sitting. From the first scene they were in (in which they are giving the French names for the garments Hector is wearing) you were drawn in, they were magnetic. I can honestly say I would have a very difficult time seeing this play with any other cast.
It was engaging in other ways as well, you don't see it in the movie but throughout the play the actors would directly address the audience. This was particularly the case for Scripps, whose narration gave his character much more depth than I think comes across in the movie.
There is not a character in the play/movie which is perfect. They are all flawed in their own way but flawed in a way which does not make them unlikable. The balance between Hector and Irwin in the play is much different from in the film, especially because they have a scene of direct confrontation concerning the "gobbets" Hector teaches the boys.
If you ask me, the thing that is most missing in the movie is that it isn't the play. After seeing the play I could never hear Bye Bye Blackbird without feeling sad. By the time it ended I was so emotionally invested in the boys (more so than the adults although I loved them as well) that if they hadn't told me about their futures I would have been upset.
To go along with this though, I have spent the better part of my academic career studying history, and while I cannot say that I knew people who were exactly like the characters in the play every time I see the scene where they discuss "can you discuss the Holocaust?" I could swear to you that it was taken directly out of classes I have been in. I admit that for me the History Boys concerns everything I love: history, education, and england, but I will always love the play more than the film. I saw every incarnation of the Broadway cast (meaning when Frances, Richard, and Clive were out at various points, I saw their replacements) and nothing touched the original cast.
I doubt that this could help at all, but every time I went there were new layers to the characters and to the play itself which I became more drawn to. I do think the play was more engaging, and that it did play better there. If there'd been a way to include some of the cut scenes for the movie I am sure they would have done it. That said, if the play opened again tomorrow with a cast I liked I am sure I'd be one of the first people there.
And hang on, when did you win the discus?