Mike Brown got the job by being "presidential" in his meetings, he talked up how he came from the San Antonio/Pop school of hard nosed defense and how his staff successfully utilized a dual big post-up offense. Which was important for Jimmy Buss, considering his hard on for Bynum at the time.
When that offense failed, Mike Brown brought Eddie Jordan on board and was devoted to installing some Princeton sets. The Lakers gave that 4-5 games before giving him the axe and taking the guy who would best suit Nash's game in D'Antoni. The 2 failed but both were a stark contrast in styles. Now with Byron, they went back to a defensive minded coach who ALSO plans on installing some Princeton sets.
Now Byron Scott should be an upgrade on Mike Brown, I just find it funny how the Lakers have come full circle so quickly. Has any team fired a coach for installing a system they didn't approve of, try something else, and then decide they liked the original format better. I get the feeling that the Lakers are making moves based on sentiment more than anything.