Computer. No question about it. If for no other reason, because it prevents math errors, and always transfers the correct amount to the correct place. The IRS says that most problems with returns are due to simple math errors. At the conclusion of filling out your taxes on the computer, the program will do an integrity check to make sure there are no errors.
In the early days, I tried a number of different tax programs, sometimes doing the taxes twice on two different programs for a direct comparison. In my opinion, there is only one choice - TurboTax. One interesting fact is that the TurboTax folks work so closely with the IRS folks, that the TT folks have pointed out errors in the returns to the IRS, and the IRS has made corrections.
I also use Quicken, but I don't import my Quicken data into TurboTax. I found that if I made any errors in categorizing the Quicken data, it will mess up my return. Instead, I use Quicken reports as my reference, and enter all the data into TT myself. If I receive any W2's, 1099's, or other statements, I use the number on the statements rather than my Quicken data -- that way, the numbers always match the statements already filed with the IRS. If I ever found an error on a statement, I'd request a new statement rather than trying to correct it myself on the return -- that would just flag it.
The IRS never releases information about how they flag returns, but I'm certain they do a lot less checking when the return is filed through a legitimate tax computer program they trust, because they know the odds are that there will be no math errors. Above all, I try to avoid having my return flagged for any reason. I've never been audited (knock on wood). It's not that there is anything wrong with my returns (there isn't); I just don't want the hassle.