Bomberman Hero is more advanced in terms of gameplay, as well as having more levels, bosses, weapons, and character moves. However, it lacks multiplayer and therefore focuses on the single player action. The game controls very differently from Bomberman 64. In Hero the character can jump, has a life meter, faces tougher bosses, and has the ability to throw bombs farther, thus, making Hero a more platform oriented experience. There are several different areas to be encountered, each with about five different stages. A unique feature is that it's possible to play with an extra advancement, such as a jet pack or a submarine.
Source: Wikipedia, Bomberman Hero , available under the CC-BY-SA License.