Smith isn't facing a lot of pressure; he is only asked to manage the game and avoid turnovers. He has the luxury of playing on a team with a great defense. This allows him to play cautiously and not force the football.
He is not expected to win games all by himself.
Sam Bradford doesn't have nearly the amount of weapons as Smith. His top target is the recently acquired Brandon Lloyd. Before that, he had to rely on players like Danario Alexander. All quarterbacks need to be surrounded by playmakers, especially young quarterbacks.
Alex Smith also benefits from the play-calling of Jim Harbaugh. The 49ers focus on running the football, which draws defenders out of coverage. Smith is often throwing into single coverage, making it a lot easier to identify the mismatch.
Bradford is forced to play in a more pass-oriented offense. Josh McDaniels likes to spread the field and attack through the air. This puts more pressure on the quarterback to move the offense. He is expected to distribute the ball and make good decisions.
For example, Bradford has 30 more passing attempts than Smith, despite playing in two fewer games. The more passes you attempt, the more likely a mistake can occur.
Last season, Bradford ran a west coast-style offense, where he excelled. Smith is in a similar offense this season and is also excelling. I honestly feel that a lot of Bradford's struggles can be attributed to the offensive play-calling.
Smith may be having a career year, but he is still not as talented as Bradford.
Even with his success this season, Smith appears to be nothing more than a caretaker. Bradford has shown the ability to win games on his own—something Smith has never shown.