This series has no reviews, so I figured I might as well write one, as it's a favorite of mine.
Story:
Admittedly, not the strongest part of this anime. It's very much a slice-of-life series, and that's not one of my favorite genres. With a few exceptions, I have a hard time staying interested in a series with no overall objective. There is a little bit of plot, but the series probably would have been stronger if it jumped into it earlier on.
Art:
I love the art. Besides just being plain cute (expected from the same designer responsible for Powerpuff Girls Z) the designs are very unique. Some of the characters have crazy hair, such as Striker's scythe and Number Nine's fish head. The art generally flows well too. There are a few episodes where the quality is noticeably lower, but generally, there's nothing distracting at least.
The series also uses a lot of CG. Again, something I'm not particularly fond of, but the anime art makes up for it.
Sound:
The BGMs aren't particularly notable, but very rarely does a soundtrack stand out for me, so I wouldn't judge it too harshly for that. The OP song is pretty catchy, though it's unfortunately accompanied with a rather bland animation that feels pretty outdated by the end of the series. There's also another song on the OP single, which is played as an insert song a couple times, and is much catchier. Both EDs really stand out, however. They're very cute songs, and appropriate for the show, as they're supposedly performed by the idol character, My Sunshine. The second actually is sung by her seiyuu.
When it comes to voice acting, as a seiyuu lover, I was a bit disappointed to see a mostly new cast. However, I've come to like some of these voice actors. Mutsumi Tamura and Kaya Miyake (the seiyuu for Bashin and J) sound convincingly enough like 12-year-old boys. Sometimes I have an issue with cross-dressing voices, as the guys can just sound too feminine for their age. Riki Kitazawa (Card Sensei) had no major anime roles prior to Battle Spirits, but has shown a nice range of emotion (going from comic relief scenes to quite serious ones) and I really hope to hear more from him soon.
Character: Probably the strongest thing in this anime. The characters are amazingly fun. I have a hard time disliking any of them. They all have some interesting quirks, and are likable in their own way. Bashin, the protagonist, is typical of a shounen hero. He's very hot-blooded, persistent, and clueless. While this is a character archetype that tends to annoy me, I found him so absolutely braindead that it can be hilarious. While they're not my number one favorites, Bashin's rival J and childhood friend Meganeko are probably the two strongest characters. Both get a great deal of development throughout the series, in ways I didn't expect. Personally, I'm a huge fan of the villains, Thousand Spirits Group. They're quite unique (it's not every day the creator of a TCG is put in it's anime adaptation as an antagonist), and for a lot of them, "villain" is probably too harsh a word. Not to say they're all nice though. Smile in particular makes a great villain, as his appearance and obsession with J come off as quite creepy.
Enjoyment: The series gets better as it goes on, with the second half being much more interesting than the first. The first episode is perhaps the slowest in the series, unfortunately. The 3+ minute long arena building scene does not help. But as it went on, the atmosphere really drew me in. It can be kind of a relaxing show, the type where I like to just marathon it to kill time and laugh a bit.
Overall: Clearly, this isn't an anime for everyone. But I certainly wouldn't limit it to fans of the TCG only, as I had never played the game before I watched this, and still enjoyed it. If you like cute, funny anime (this series has made me laugh out loud countless times) you'd probably enjoy this. If you prefer your anime with a gritty look and a dark, serious plot, you'll probably hate this.