I am a huge admirer of both these journalists and use Snow's twitter feed as a great source of digestible information.
During the interview (4min45seconds) Snow describes twitter as 'heralding the golden age of journalism' and it provides an opportunity to 'lead people to water'.
The key to twitter, as described by Snow, is not to tweet a picture of your cup of tea (as Paxman claims is the only thing he could think to tweet about) but a link to something of value.
I sympathise with Paxman's claim that 'twitter is for people with nothing going on in their lives' because he, like many, do not have time to produce digestible and relevant insights to their audience. However I completely disagree that he does not have anything to share, like many knowledge-rich, time-poor experts this is a misconception and barrier.
Paxman and Snow do agree on one thing, twitter is a great source of information and if you are not contributing, it is at the very least worth consuming.