Lostorage Incited WIXOSS

The start off of both anime are different, but the basic concept of the two involves teenagers playing a game and putting their life on the line. While both involves having a card, Lostorage involves players gaining and losing coins that would effect their memory. If a person loses all their coins in the game, their avatar would take over their body and they would lose their memories. However, if the player gained all 5 coins, then they have the option to choose a memory they would like to change.  

It's no secret that these are two anime who try to play off their plots as cute fluffy fun until it gets to a certain point and get dark. They aren't the first of their kind to do so but they are two of the most well known. Both anime girls are tempted by the promise of a wish to enter into the mysterious underlying worlds seperate from their own. And both girls are shocked to learn failure could produce a fate worse than death. The dark themes never really calm down during the course of the show either. 

- Both have to bet the coin to play the card - Have a plot that make protagonist wish granted. - Both play Card game with similar mechanic and playstyle. 

Holy Grail War Styled Theme minus the trading cards for one and the magic (mostly) for the other 

A bit of a stretch. Story lines aren't similar, but the theme of despair fuels despair is prevalent in both. 

though lostorage has more of a card system, angelic layer is very similar in avatar battle system and also focuses on the battlers' personal struggles. 

These two anime revolve around friendship, losing it and working hard to restore it back to where it used to, but this time, only better. Both main characters of the two shows' motivations to achieve their goal are somehow similar as well. Chances are, if you liked the friendship concept of either, then you'll probably like the other as well. 

While these two shows have many things in common when it comes to tone (though Wixoss is quite the bit darker) and setting, with a big modern city and dark magical elements, the main reason for this recommendation is the duality of Izaya (Durarara) and Satomi (Wixoss). Both characters serve as driving forces from behind the shadows in their shows, and have similar motivations and personalities. I think that, if you like one show specifically for that elemenent, you'll definitely like the other.