Twitter can be an effective way to share links. However, its effectiveness is entirely dependent on the number of followers you have (and the quality of those followers). If you only have 5 followers, don't expect to get a lot of traction. For example, Jason and Dharmesh will have way better results on Twitter than me because they have thouasands of followers, whereas I have less than 20.
So to answer your question on how effective Twitter is compared to other techniques...It depends. If you have
more fans on Facebook than you do followers on Twitter, your chances for sucess are higher on Facebook. And vice versa.
But don't let this stop you if you only have a few followers. The way to increase your followership is by sharing good, useful information. So share your links, and slowly over time the number of people following you will increase...Making it an effective way of communication.
Also, you asked about what circumstances make Twitter a good channel. The answer is when your target audience uses it. For example, if you're selling the Jitterbug (a cell phone with gigantic keys for the elderly), don't waste your time on Twitter because odds are your audience has probaby never even heard of Twitter. Of course this is an exaggerated example, but I hope it illustrates my point. On the flip side, Twitter is really effective with the tech crowd.
I hope this helps!
I agree with everything Zuly said, I'd upvote but I am new here! I just wanted to add, that it's still a good tool even if you have only a few followers IF those followers are evangelist. If they are, then they can "retweet" your tweet to their followers, thereby spreading your link even further. If your like is of high quality, there is always potential it gets retweeted by people further down in the chain as well.
Links via Twitter are limited by the amount of time they would be available. Which is all right for something more up-to-the-minute, but not for something permanent.
Other than that, I think it has to do with the method you've setup that has the most reach. Could be your own website, Facebook page, emailed newsletter etc.