If you're looking for anime similar to Battle Spirits: Kakumei no Galette, you might like these titles.
Upon the conclusion of the Vanguard High School Koshien, Kouji Ibuki begins to have new nightmares. Nome Tatsunagi has Suiko summon him to the mansion where they learn he can see a Dark Tower called Sanctuary. Sanctuary is causing the timeline to be altered throughout history, and the only way to correct it is for Kouji to first correct his future mistake. Now Kouji and Suiko must travel the parallel world -if- and watch as Magical Girls Emi Sendou and Shuka summon Vanguard units to help correct history. Sadly the two can't help much as Cardfighting against real monsters doesn't do much good.
If you'd rather your card game anime are probably more complicated than they need to be, then check out either of these. They're not simply about card tournaments, but have other problems with higher consequences than simply losing a match. They're both also spin-off os popular franchises, and are based off real-life card games.
Yu-yu is a boy living in Kanazawa, Kaga Province. He is 15 years old and in his third year of junior high school. He has the ability to sense the feeling of others, but he is troubled by the fact that he cannot say no when asked. One day, Yu-yu could no longer stand going along with his sister's hobby, so he ran away from home. The one who saves him is Megumi Okura. Megumi invites Yu-yu to a nighttime amusement park called "Wonder Hill" where her friends hang out. At the amusement park, Yu-yu meets Megumi, Zakusa Ishikame, and Tomari Seto, members of "Team Blackout," a group that meets to play Vanguard every night. Tonight, a serious fight for the team's flag will take place. Blackout's leader, Danji Momoyama, and the mysterious and powerful fighter, Tohya Ebata. As Yu-yu stares at them, the card fight is soon eroded into a world of images. This is how Yu-yu encounters Vanguard, a world he has never seen before, and is drawn by its powerful allure - making new friends along the way.
In the near future, a battle card game called "Battle Spirits" has gained enormous popularity. Players of the game -- known as "Battlers" -- start duelings everywhere using their color-coded cards with different attributes, creating a "Sengoku (Warring States) period" for the game.