True Blood, which is novel based has become HBO's biggest summer hit. - the entire first season of the HBO show was based upon the first book in the series called Dead Until Dark (The Southern Vampire Mysteries, Book 1) by Charlaine Harris. The Sookie Stackhouse novels has a rabid and devoted fan-base. See True Blood on Twitter http://truebloodtwitter.net/
Sookie Stackhouse is a young, intelligent, and extra-sensory perception wielding southern lady. Sookie has rejected the advances of men she has known since she states "it's hard dating regular guys when you know what they're thinkin'." (that is, until she meets her charming, romantic, vampiric counterpart).
The most obvious difference, at the out-set, between the two stories and the worlds that Bella and Sookie live in is the fact that, in Sookie's world, vampires are commonly known to exist, and they are openly trying to assimilate into human society (for the most part, at least). The clever name of the television series, in fact, comes from the title of the bottled blood that vampires (are supposed to) live off of. In Twilight, by sharp contrast, the world is mostly unaware of the existence of vampires, and the vampires that do exist (save for the Cullens and the Denali clan) are mostly nomadic and do not try to resist their thirst.
Sookie (played by Oscar-winner Anna Paquin) is eager to become affiliated with vampires, and when she meets Bill, she, like Bella Swan, is totally enamored with him. Unlike Bella, Sookie can let Bill bite her without necessarily becoming a vampire as the procedure for "the change" is quite different between these two stories.
Bill (played by British Stephen Moyer) is a bit like Edward Cullen (played by also-British actor Robert Pattinson) in that he is frustrated with his circumstances as a vampire and wants to be different from some of the less human-friendly others of his kind. Edward comes across as a tortured vampire, where Bill just seems uptight.
Also, there is another similarity. In True Blood, as in The Twilight Saga: New Moon, there are also shape-shifting (werewolves, arguably) humans such as Sam (played by Sam Trammell) and Twilight's Jacob Black (Taylor Lautner). Although in the Sookie Stackhouse Novels there are much more than just werewolves.
Perhaps most obviously, one similarity between these two series (book and TV/film) is the fact that the protagonist is a woman, who carries a voice and virtue that her audience can identify with. Her relationships with vampires in the stories is trying, at times, but for the most part one which she wants and finds love and comfort within. Both Sookie and Bella have a uniqueness about them and when they meet their vampiric counterparts their lives change forever.
As for the actors, Anna Paquin delivers in True Blood. She is able to present the southern sweet belle charm at the out-set so well, but also maintain that consistent edge that Sookie Stackhouse has. In other words, she is sweet, but she has a low tolerance for bull all the same. Kristen Stewart, similarly, presents us with a Bella Swan which we can recognize from the book series - inward, thoughtful and intelligent, learned, and constantly in awe of her leading man. Stephen Moyer effectively presents the inner struggle that his character has as well as the consuming desire to protect Sookie in True Blood. One could literally feel his pain as he lay in wait (because, in True Blood, vampires cannot come out in the sun, and, in the south, cloud coverage is not helpful) to come to Sookie's rescue. Robert Pattinson's performance of Edward Cullen runs through a similar vein - the viewer can identify with the washes of strife that come across his face, but are taken by his cavalier and courtesy throughout the story.
Both of these vampiric stories have elements that, at times seem to mirror each other but, once you sit and digest the differences of these books, the more you can love both series for what they are. Twilight is aimed more toward the teen crowd while True Blood is definately more adult oriented and to be honest, reading the books aimed toward the younger crowds made me feel pervish and I do not feel like a perv for lusting after the Vampire Viking Sheriff Eric Northman.