This is the movie that made John Woo the reputation that he has for action films. If you enjoy action films, and in particular other Hong Kong action films then you will enjoy this. Stylistically it is easily identified as a Woo film and doesn't really transcend the action film genre but it does work marvelously within the confines of that genre.
Some consider The Killer or Hard-Boiled to be the better John Woo HK film but I find that while the Killer and Hard-Boiled both have tighter, more elegant action sequences what really makes A Better Tomorrow lead the pack is the plot. It isn't an entirely original plot but it is well acted enough that you really feel for the characters and can understand the motivations. It isn't a typical action movie plot where the script serves simply as a device to create interesting action sequences. You get traditional Chinese themes such as honor, loyalty, and strong family ties.
As always Chow Yun Fat is a pleasure to watch. He is simply one of the coolest action stars in the entire global movie industry. You could search far and wide and not find a more suave action star than the dual-pistol wielding, cigarette-in-mouth Chow Yun Fat. Worth watching for his presence alone. If you only know him from the American films he has done then you are doing yourself a disservice.
In summation: if you like action films you will love A Better Tomorrow. It's that simple. Also check out other Woo HK films like The Killer and Hard Boiled.