Here is a list of Pac12 Championships won by Oregon:
1994
2000
2001
2009
2010
2011
2014
2019
2020
Running off this premise, Oregon and USC are both tied at 9 titles. However, USC's run with Carroll is far more memorable than any of Oregon's run (the Chip Kelly run was memorable though and I will explain later).
USC went on the road and won a lot of big games beating Ohio State 2x, Auburn 2x, Arkansas 2x, Michigan, Notre Dame multiple times, Nebraska 2x, etc.
USC went out and played everyone. They also had a pretty strong dominance of the Pac12 itself during that period.
Oregon hasn't gone on the road as much to win big games. In fact, most of their big road games have ended up with Ls such as LSU in 2011 or Auburn in 2019. The exception is the win at Ohio State this year.
Another key factor is that Oregon hasn't won a title yet although they were very close in the 2011-2012 season and in 2014. USC had the best talent, put it on display in major road games to East Coast opponents, and won at a very high level. Oregon tends to win a lot of games but often struggles when they meet that higher crop of teams on the East Coast. There also isn't a major opponent in the Pac12 to create big-time matchups and eyeballs for Oregon. UCLA was the closest opportunity this year in the Pac12 and they have kind of fallen a part since their matchup with Oregon.
USC also tended to put more big-name players in the NFL.
All of these points are why USC tends to get a lot more respect than Oregon on the National Scene despite the fact Oregon has been a better program this decade.