Re: 1981-1998 San Francisco 49ers vs 2001-2018 New England Patriots
Patriots play in the NFL's softest division (no other team in it has been to the SB since the early 90s), so they not only have an easy path to winning the division, but rack up a lot of easy wins, so usually get a first round bye. Then they are just one home win away from playing in the AFC championship game. And they are 20-3 at home in the B-B era, but only 3-4 on the road.
In the 80s and early 90s, the NFC was much better than the AFC--they won 13 consecutive SBs--so it was much harder to get to the SB, though relatively easy to win once you got there.