Well, really where is the comparison, West Ham are a team fighting for Premiership mediocrity, and Millwall are a small pathetic club in the lower reaches of the lower levels of English football. Both teams support comes from similar areas of London, and both clubs have been plagued by hooligan support, Millwall's is well documented, and West Ham's hasn't been slow in fighting at any oppotunity, indeed, a young lady, Cassandra Pennant, wrote a book about their gang, the Ice Cream Factory I believe them to be called
Yet surprisingly, we are able to compare the clubs this century.
They've played each other in 4 league games, resulting in 2 1-1 draws at the home of the Irons, and 2 Millwall victories, by 1-0 and 4-1 at the Lions stadium. So, Millwall comfortably win this comparison.
Both teams have made the play off's in the Championship, Millwall, who finished 4th, rather unluckily failed to get promoted, yet West Ham, finishing 6th, had the good luck to win them. Pretty even there.
Millwall also won the title of a lower division, as well as making the play offs, but thiis really counts for nothing when comparing to the Hammers.
This century both teams have had one surprising national success, making the FACup final, both failing in the final hurdle, losing to a big4 team, West Ham losing to what is generally considered to be the weakest of the big4, Liverpool, while Millwall had the missfortune to come up against probably the stronger of the big4 in Manchester United. Again, not much difference between the clubs there.
Having failed to win the cup, both teams entered the Uefa cup, West Ham losing both their games, while Millwall managed to win a point for the English coefficient. So, finally, there's a somewhat startling difference between them. Millwall have been better in Europe, for England than West Ham.