Which is most important somewhat depends on which one you prefer. If you prefer one over the other, then that's what you should go with as your enthusiasm for that platform will easily come through. I find that both have their advantages not only for marketing and networking but also for
SEO.
I do not typically post the same information to both as I think that's redundant and goes against the idea of being "social." I also don't have it auto set up for posts from Facebook going to Twitter or vice versa. For the same reason...they are two different platforms that operate differently and people who see your post from Facebook on Twitter aren't necessarily going to have the right context. As well as posts from Twitter don't generally lend themselves well as an update from Twitter. Plus if you are prolific tweeter then this gets overwhelming for your friends/fans on Facebook. Sometimes there is value in shooting an update from Twitter to FB using something like Hootsuite but I find I use that more for convenience than for auto updating everything or scheduling a bunch of tweets to FB.
I do have some clients who do have it set up so FB posts go directly to Twitter and it works okay because those clients are putting in updates that ask questions or that are conversational enough to elicit good responses from either platform.
All that said, I think is some value in scheduling tweets or updates as way to help keep the account current and to help with some of time management involved in using social media. I don't think, though, that this should be the ONLY way that the accounts are updated.