A friend recently asked me if he should use Twitter.com or a specialized program or website to engage with the Twitterverse. Here is my reply:
While Twitter is quickly updating their service to make their website more useful for tweeting, I would still recommend a service like TweetDeck or Hootsuite.com to manage your Twitter account for anything but the most basic experience.
For managing all the ongoing conversation, these apps allow you to organize the people you follow into groups and even set up saved searches (e.g. a perpetual search for anyone mentioning your company or favorite charity). TweetDeck and Hootsuite both let you organize tweets and twitters into multiple columns. TweetDeck lets you set pop-up notifications for particular columns so you can keep an eye on high priority items. TweetDeck is a desktop (and mobile) application that has to be open to run. Hootsuite is a website that lets you manage your conversation in the browser (think of it as Outlook vs Gmail, in a way).
On the tweeting site, these services allow you to easily add video, images, short URLs and other Twitter niceties that are offered by third-party services (i.e. not directly from Twitter) that have become an integral part of using Twitter. Additionally, these services allow users to manage multiple Twitter accounts (and even accounts from other networks, like Facebook & Foursquare).
The bottom line is, Twitter.com is sufficient for a very infrequent, basic user. But for anything more, you need to use a specialized Twitter client.