The first Bayonetta was what helped set the developer Platinum Games on the list today and their tendency to make great gameplay. While Bayonetta's gameplay is basically spam dodge and mash attack to win, the variety in combos and the diversity from the weapons you acquire is what makes the experience so memorable.
Another PG game quality feature are their boss fights, and this is very apparent in Bayonetta. They seem really keen on making these fights look "epic" and "stupid" at the same time, but in the end, are really fun and not entirely QTE-fests(while this should be looked at, other developers could learn well from them).
Bayonetta's blatant fanservice isn't limited to franchise only. I recently finished my Club Nintendo copy of Wonderful 101 and I'm pretty sure the unnecessary skin-tight ass camera panning shots is more of a PG thing.
When it comes to story, Bayonetta's story is very vague, but develops the amnesia-stricken Umbra witch well nonetheless - cliche as the archetype is. When the answers are revealed practically AT THE END of the game before the final battle, it...it ties together nicely in a way.
Sadly, Bayonetta 2's story is definitely not as engaging, and more cliche-ridden than the first game - leaving me the impression that a sequel was something not in the original plan, especially since the first game's story and it's lack of gaping plot holes leaves little for a sequel. However, Bayonetta 2's gameplay seems to make up for it, at least from my experience - also, online play on a Nintendo console.