casual movie fans will prefer Nolan where as snobbish movie fans will prefer Anderson. both are good, but are like comparing apples to oranges.
critically they are both very similar, but financially there is no comparison. Nolan's movies consistently make money where as most of Anderson's movies flop.
Oscar Nominations/Wins:
PTA (6 nominations, 0 wins)
Best Writing, Adapted Screenplay (Inherent Vice 2014)
Best Motion Picture of the Year (There Will Be Blood 2007)
Best Achievement in Directing (There Will Be Blood 2007)
Best Writing, Adapted Screenplay (There Will Be Blood 2007)
Best Writing, Screenplay Written Directly for the Screen (Magnolia 1999)
Best Writing, Screenplay Written Directly for the Screen (Boogie Nights 1997)
Nolan (3 nominations, 0 wins)
Best Motion Picture of the Year (Inception 2010)
Best Writing, Original Screenplay (Inception 2010)
Best Writing, Screenplay Written Directly for the Screen (Memento 2000)
Box Office Numbers and Rotten Tomato Critic Scores for PTA
Hard Eight (1996)
budget: unknown
box office: 222k
RT score: 83%
Boogie Nights (1997)
budget: 15M
box office: 43M
RT score: 92%
Magnolia (1999)
budget: 37M
box office: 48M
RT score:84%
Punch-Drunk Love (2002)
budget: 25M
box office: 24M
RT score: 79%
There Will Be Blood (2007)
budget: 25M
box office: 76M
RT score:91%
The Master (2012)
budget: 32M
box office: 28M
RT score: 85%
Inherent Vice (2014)
budget: 20M
box office: 11M
RT score: 72%
Box Office Numbers and Rotten Tomato Critic Scores for Nolan
Following (1998)
budget: 6k
box office: 240k
RT score: 78%
Memento (2000)
budget: 9M
box office: 40M
RT score: 92%
Insomnia (2002)
budget: 46M
box office: 113M
RT score: 92%
Batman Begins (2005)
budget: 150M
box office: 374M
RT score: 85%
The Prestige (2006)
budget: 40M
box office: 109M
RT score: 76%
The Dark Knight (2008)
budget: 185M
box office: 1.004Billion
RT score: 94%
Inception (2010)
budget: 160M
box office: 825M
RT score: 86%
The Dark Knight Rises (2012)
budget: 230M
box office: 1.084Billion
RT score: 88%
Interstellar (2014)
budget: 165M
box office: 672M
RT score: 72%