The anime is pretty fun and despite everyone and their mother saying its pure fanservice, truth is that is pretty subdued for today's standards (no full frontal nudity and panty shots are actually scarce). The story is certainly inferior to the one on the game but is a great introduction to the series, I got hooked on the series with the anime in fact.
The Vita game is, weird. It leans more towards the Musou genre and while technically is superior to Burst, the long loading times and bad camera put a huge damper on my enjoyment of it. Is also pretty repetitve and the story is one of the worst of the series. Good for a mindless button masher but nothing more.
If anything, I got way more enjoyment from the rhythm spinoff.
And definitely pick up the second game, easily one of the best third party games on the 3DS.