North Carolina always has close Senate elections. Elizabeth Dole's defeat was primarily because she was ineffective and invisible as a Senator, and when she was visible it wasn't good (chairman of the RNSC). Not to mention that she had no real background in the state. She hadn't been a resident for forty years when she came down here and has probably been in Washington longer than anyone else. The 'godless' ad clinched it and might have actually helped her out if she hadn't had an impersonator voice "There is no God!" Whoever ran the ad must have been intentionally trying to sabotage the campaign. Instead of raising the issue "Why is Hagan getting support from these people?" (a legitimate question) the focus of discussion was how desperate Dole was to mislead people about Hagan. After that ad there was no hope for the Dole campaign, which had already been losing early voting - the reason the ad had been run in the first place.
Burr is a better candidate than Dole. For one thing, he actually has a base in the state and is liked among conservatives, who were lukewarm about Dole. I would give him the advantage in 2010 over anyone other than Roy Cooper or Heath Shuler - except for the fact that his seat is cursed. But that's okay, we'll win the seat back in 2016.
Burr does have a stronger base than Dole did, but it wasn't like the conservatives voted for Hagan, they voted for Dole. Dole got demolished among moderates (64-33), Burr's base is not going to help with that. Obviously a lot will depend on the candidate and the overall political climated a year and a half from now. However, unless the economic situation is far worse than it is now and Obama is very unpopular, I think its going to be a real tough fight for Burr. If things are starting to improve or Obama's approvals are even remotely near where they are now, Burr will be in deep, unless the Dems nominate a terrible candidate which seems highly unlikely given the bench.