sure combining Facebook and Twitter strategies is the best! i do that lately and I'm getting good results, previously i thought twitter was not good but after few months of working with it I can understand why it's getting so famous
twitter because it's better and facebook has lots of privacy issues. (for example, they gave out my phone number on other sites without my authorization!)
I don't think you can really compare facebook and twitter. Twitter is essentially the same thing as facebook but it is only status updates, just a much more simplified network. Facebook is much more interesting and definitely more addictive. I also don't think you can really say that Twitter is for business either. Businesses can of course use both of them to promote themselves and Twitter is definitely a great way to let customers know about deals and specials but Facebook is a great way to show people what your business is about along with letting them know your promotions. Twitter can never replace facebook unless it expands to what facebook is with real profiles and photo galleries and games and such. I prefer Facebook over Twitter because like some others said, Twitter annoys me.
I think Twitter is best for business, particularly if you have a targeted twitter username and a relevant twitterfeed. Facebook... not so go good for business imo.
I'd say to combine both, as they'll have a synergistic effect that'll really boost your social media and marketing exposure.
I prefer Facebook, I think it is much better in terms of marketing as compared to twitter. I use continuously both, but haven't seen any benefit of twitter yet.