Up until now I've generally been checking out the anime first, but that's more due to the fact that I can rent DVDs, but I have to buy the manga (my local library doesn't really stock any).
I have been let down a couple of times by this now, though. Most strikingly is Peacemaker, the first manga (Shinsengumi Imon Peacemaker) keeps a very tight storyline and plot, whilst the anime throws in all these weird, out of place mystical plotlines (think they're from the second manga).
More annoyingly there was the Fruits Basket anime. I love it, it's funny and sweet, but the ending's a cop-out, and it has so much less depth than the manga. That's the thing I generally find, that the manga is deeper and more involved than the anime. I know this will mainly be due to time and budget restraints, but sometimes I can't help but wonder why they've discarded a perfectly good plot twist in favour of something improbable and ridiculous (some of the changes to arcs from the first Rurouni Kenshin series are a case in point)
So, from now on, I'm going to go for what came first if I can. This also goes for prose novels, I've just started on the Vampire Hunter D series, which they started translating and releasing last year. I'd love to read the originals, but my Japanese isn't good enough to tackle prose yet. :cry: