The sequel of Matrimelee. It features enhanced graphics and sound, the return of two of the older characters (Angela Belti and Kinta Kokuin), a new boss, and the return of the transformation feature. Gameplay was also improved in some areas, and super attacks were made easier to execute.
The game also features an online mode and a 'Lust Cards System' that consists of buying cards with special effects. Some allow the player to change certain characteristics of the characters, others are used to view special music video clips, and others to call strange characters to help the player in battle.
The game has the same backgrounds and all the characters from Matrimelee, and because of that it is usually described as a port of the game, while in fact the game's story takes place after the events from the previous game, making it a sort of sequel or update.
Bonnou Kaihou was released only in Japan, much to the chagrin of international fans. It is possible that this is due to the very little chance of marketing the series ever had outside of its country of origin. Ignition, a company that helped to publish the game, has explained there are currently no plans to release the game outside of Japan. The subtitle Bonnou Kaihou literally means "Liberation of Lusts".
Source: Wikipedia, "Power Instinct", available under the CC-BY-SA License.