Facebook is better because lots of free facebook applications and games to spend time and to grow friends circle. You can also find old and new friends there.
I like facebook for sharing website, images, videos, any type of news and articles. This is really very nice.
Facebook is more popular and has more content. If you have a Facebook Group/Company/Fan page, you can actually link it to Twitter, so your posts show up on both your facebook fan page and twitter.
Twitter used to be the best because of its minamalism approach, without the fancy extra features. But now it is mainly spammers, so facebook is now the better.
Agreed, they were not designed for the same niche. If you want to keep track of your friends, use facebook. If you want to track your friends down somewhere, twitter would be a better option.
I run an Occult Forum and people there kinda like their privacy. Many of them use both Twitter and Facebook, but many of those that do use both will ONLY discuss the occult on their twitter accounts... why? Because they don't want their parents or co-workers knowing they dabble with darker forces then main stream gods.... So for me, Twitter is MUCH better... but I have recently started more integration with Facebook which is doing well. But as AMiRU said, they are two entirely different things, both used for entirely different reasons...so there really is NO comparison.
I can't really decide between FaceBook and Twitter. Both are great social networking websites. In the past, I used FaceBook but since I found Twitter, I've liked it ever since.