Change football a lot I think. The Pats don't become the dominate team of the last 17 years that they are now. Bill Belichick might not be as much of a success. The Niners return to the dominate team that they were under Montana/Young.
The Niners drafting Brady would happen at pick 150 in the 5th round since they did not have a sixth round pick.
In the third round they picked Giovanni Carmazzi (taken Brady two rounds later would not change this) what would change with is I doubt Tim Rattay gets drafted in the 7th round by the Niners. So maybe the Pats draft him? Of the two QB's the niners took that Draft he was the better player honestly.
If the 49ers take Tom at 150 like you said, then the Pats turn to Rattay in Round 6 (Belichick was interested in him).
As for Brady, he beats out Gio for the second-string job behind Garcia, and that's where he stays from 2000-03.
By 2004, though, Garcia goes to Cleveland. Brady, who is a better fit for Dennis Erickson's offense (spread) than he was Mariucci's (WCO), gets the keys to the car. In OTL, the Niners were 2-14 that year with Rattay and Ken Dorsey at QB (they had 12 losses by eight points or more). With Brady, I see them going 4-12, but no better. They were a bad football team. That would give them the third pick behind Miami and Cleveland.
After the Dolphins take Alex Smith #1 overall, and the Browns take Braylon Edwards at 2, the Niners are up next. After failing to complete a trade with SD that would have given them Drew Brees for the third pick, the Niners settle for A-Rod (new regimes mean new coaches, and they would still hire Nolan as HC after firing Erickson).
Brady stays as starter for the next two seasons. He shows potential, but the 49ers win only five games in 2005 and eight in 2006.
By 2007, the 49ers and Mike Nolan are ready to hand A-Rod the ball. They added him some help in recent years in guys like Vernon Davis and Frank Gore, but they have more work to do. As for Brady, he asks for a trade, and gets moved to the Patriots, a team that was high on him back in 2000. Bledsoe retired by 2004, and Tim Rattay didn't work out.
Brady would play better in New England, but he did pick up a bad habit or two playing on a bad 49er team. Belichick is going to have his work cut out for him.
The fundamental problem the 49ers had in the early 2000s isn't the quarterback position, it's the impending retirement of Bill Walsh as GM. His successor, Donahue, not only got Mariucci fired in a power struggle but also oversaw the 49ers sliding from a 10-6 team in need of a reload to a 2-14 team that would be in rebuilding mode for the next six years. Brady himself would have an interesting career arc; a good QB stuck on a bad team who would probably end up being traded or let walk in free agency in the mid-late 2000s. Depending on the team he ends up at, he remains a good QB on bad teams, or has a Drew Brees-esque flowering.
Luckily for him, there should be at least a couple good teams by that point looking for a new QB who would be willing to take a flyer on him. The Patriots are actually a good candidate; Drew Bledsoe will be close to retirement by then. Depending on where Rodgers ends up, the Packers are another candidate. Hell, if Sean Payton still ends up in New Orleans, maybe he'll go there. Lots of possibilities.