It's not about your anonymity, but about your audience. As @darkf mentioned, Twitter doesn't have the same level of privacy settings that Facebook does. A user's tweets are either all protected or all public. This means that you have less control over your audience. A message that you meant as a sarcastic comment could be retweeted (repeated with attribution) by a friend who thinks it is funny, but someone you don't know could miss the sarcasm and interpret it as a terroristic threat and report it to the authorities. At this point, because of the public nature of Twitter, the authorities do not need a warrant or a subpoena to view your statement; depending on the level of personal detail in your profile, they might not even need Twitter's cooperation to identify you directly.
Facebook's privacy settings are really not any protection against law enforcement, since Facebook will comply with legal requests to access your content. Its real "benefit" in this situation is your ability to control your audience: if only your friends see your sarcastic statement, it is much less likely that they will turn you in to the authorities for making terroristic threats, since they are more likely to understand your tone and the unlikelihood that you are seriously making a threat.
EDITED TO ADD:
I didn't address Reddit. Because a large part of its structure is as a link aggregator, the opinions and statements of its users are primarily found in the comments, a lower-status area that doesn't get as much attention for a few reasons:
- Perception based on other sites that the comments section consists of loonies.
- Reduced ability to search comments for terms of interest. (Does Reddit even offer this natively?)
- Widespread use of joke or throwaway accounts.
In other words, the signal-to-noise ratio is too high to make monitoring Reddit (or taking threats there seriously) of much worth to law enforcement. Twitter is really in the sweet spot between strong identity links (people using their real names and investing in their account's status) and openness of content to observation. Twitter's API even makes it easy to monitor for threats: you could have a feed consisting solely of tweets using the word "bomb" that originate in Birmingham, for instance.