This is only season 1, by the way. It ends on a cliffhanger. Season 2 is called Selector Spread WIXOSS and was broadcast a few months later. Wikipedia also says there's going to be a movie next year (Selector Destructed WIXOSS) but I won't be worrying about that here.
Everything I'd read called this Puella Magi Madoka Magica, but for trading card game anime. I generally don't like that kind of reductive description, but it's close enough that I'll run with it here, especially since it's hard to talk about this series without using Madoka as a comparison point. The plot involves a trading card game called WIXOSS (pronounced "wikross"). The game is real and you can buy it in shops. This is always true with this genre, which is traditionally a series of 24-minute game commercials. However the characters of this fictional show aren't like you and me, because they're Selectors who can talk to magical WIXOSS cards called LRIGs.
A LRIG ("girl" backwards) is a portal to a magical girl who lives inside the card and grants wishes. The difference between this and Madoka is that LRIGs only grant wishes after you've won enough WIXOSS battles, whereas Madoka's wishes were the start of your magical girl adventures.
That's a disingenuously simplified version of the truth, obviously, but that's what the Selectors are being told. Further discussion would get us into spoiler territory, but I did think the full truth seemed perverse to me. What bastard thought that up? I'm only halfway through, though, so there's probably a bunch of stuff I've yet to discover. Besides, I think the point of the show is to explore what it means to pin your hopes on magic, when you'd be better off choosing attainable goals that you can focus on without assuming that you need a fairy godmother. Making wishes the culmination of the journey instead of their starting point is a fundamental difference from Madoka and gives the show something meaty to talk about.
Sometimes your wish is something you'd have been better off trying to achieve all by yourself. Alternatively, in other cases a wish looking unattainable might perhaps be something you should have thought about carefully. Wanting to have sex with your brother, for instance. Yes, that's in this show. That was kind of scary (and was meant to be, obviously).
Since we're comparing with Madoka, I also appreciate the fact that the Selectors aren't doomed. Complete hopelessness is rarely what I'd call a plus, although one does wonder what will happen to the LRIGs when WIXOSS stops being popular and vanishes from shops.
I quite like the cast. The main girl, Ruko, is nice, but occasionally gets described as "scary" by people who say they've no idea what she's thinking. I'm pretty sure that's going to get followed up. She gets into WIXOSS not because she's fixated on a wish, for instance, but because she enjoys the battles. Meanwhile she's loyal to her friends, once she acquires some, but hadn't previously seen the need for any, doesn't have a mobile phone and is bad at using computers.
Yuzuki knows her wish is wrong and considered unacceptable by the world, but is aiming for it anyway. What complicates this is that she's a sympathetic (if distant) character and one of Ruko's two friends. The other is Hitoe, who's painfully timid and is just fighting because she wants friends. Gyaaaaah. Hitoe hurts.
On the other hand, there are also bitches who take pleasure in crushing and humiliating their opponents. Akira, for instance. Ruko will develop moral qualms about beating other girls in battle and helping to prevent their wishes from coming true, but quite rightly doesn't apply those to Akira.
The theme music ("killy killy JOKER") is catchy, by the way, and adds some fun to the experience of watching what's a fairly dark and serious series. I also love the watercolour-like background art, although personally I'd have preferred the design of Ruko's granny not to look so bland and anonymous.
Plot nitpick: how did Iona's tournament work in the apparently available time, since we'd previously been told that LRIGs go to sleep to recharge after battles?
This is quite a harsh show, but I wouldn't describe it as traumatic or depressing (yet). There's warmth in Ruko's relationships with her friends and family. The girls are nice. They care for each other. Yuzuki's incest fixation makes the show uncomfortable, but it's meant to be. Something horrific happens halfway through, but that's not the end of the story. I'm definitely watching season two to see where it's all going, anyway.