Card Heroes wasn't my favourite of the pair, but it seems to have a reasonably devoted following and it's good to see at least one of the Sengoku Basara mobile games continuing, especially as they're an excellent source of official illustrations in the absence of a new console game.
The relaunch will include new features, such as a twice-daily 'alliance battle', as well as new character abilities and attack modes. Existing game data will be carried across to the new version automatically. Sengoku Basara Card Heroes Matsuri is compatible with smartphones running iOS 4.0+ or Android OS 2.2+, and most featurephones from docomo, au or SoftBank compatible with Flash Lite 1.1. It's free to play (you just need to create a Mobage account), however, there are in-game purchases required for some items. The software is only available in Japanese.
The Card Heroes advertisement from back in 31st July 2012 gives an overview of how to play: