Like Dudley Dursley, Malfoy is a bully – except Malfoy is way more dangerous. He's your typical Slytherin – cunning and devious, with a tendency to use magic for cruel reasons. He sees Neville as an easy target, picking on him in order to get at Harry, but he's also mean to people like Ron and Hermione.
When Harry first meets Malfoy, it's on a semi-anonymous basis in Madame Malkin's Robe shop. Malfoy has "a pale, pointed face" (5.262) and "a bored, drawling voice" (5.265), but it's the things he says that make Harry "strongly reminded of Dudley" (5.265). In this first discussion, Malfoy shows pride in both Hogwarts houses (Slytherin) and family (old wizarding blood). He's a big talker and claims that he can "bully [his] father into getting" him a broom" (5.265) – although if you've read further in the series, you know that his dad Lucius isn't exactly the type of person you bully. Malfoy also gossips about Hagrid's reputation.
Draco immediately opens Harry's eyes to the prejudice that goes on in the wizarding world, asking Harry if his parents were "our kind" (5.183) and separating people like himself and Harry from those whose parents weren't magic-born. On the train to Hogwarts he offers Harry the chance to abandon the friends he's started making – like Ron Weasley – and hang out with him and his Slytherin friends. But in telling Harry he shouldn't hang out with "the wrong sort" (6.244) he only manages to convince Harry not to hang out with him. Of course, this makes them enemies at Hogwarts. Malfoy's insistence on separating people by their differences, and judging those who aren't like him in a negative light, is eerily similar to the Dursleys' attitude towards, and fear of, magic-wielding individuals.
Although Malfoy is always trying to get Harry in trouble, it usually backfires bigtime. In some scenarios, Harry lands on his feet, like how flying against regulations shows his potential as a great Seeker. In others cases, sure Harry gets landed with detention, but so does Malfoy.
Malfoy's more interested in messing with Harry than in standing up to him; he doesn't show up for their midnight duel, and he tattles on Harry when he overhears the plans for smuggling Hagrid's dragon Norbert out of the castle. While these seem like minor infractions compared to the real evil wielded by someone like Lord Voldemort, Malfoy's behavior shows the seeds being sown for far worse behavior as the series progresses. His dislike of Harry is only going to get worse, and his attitude about purebloods being better goes against the book's larger message about accepting differences and spreading tolerance.