The Dons have not taken three points off Motherwell for 11 games, since before Mark McGhee and then Brown left the Motherwell hotseat for Pittodrie.
But they have knocked Motherwell out of the William Hill Scottish Cup at Fir Park twice this year, the most recent occasion being a 2-1 replay win earlier this month.
However, their quarter-final victory by the same scoreline in March was followed six days later by an SPL loss in Lanarkshire when Motherwell left-back Stevie Hammell struck the only goal with a superb 30-yard strike.
Brown is therefore not sure that their recent cup exploits will have much bearing on Boxing Day.
The former Scotland boss said: "Remember last year we beat them in the cup and then we lost 1-0 to a rather fortunate long-range shot from Stevie Hammell in the league.
"We would like to do the double over Motherwell, obviously. It would give us a great platform for the remaining league fixtures if we managed to pull back the three-point gap.
"Obviously we don't want a repeat of the last experience, although in the league you can recover and in the cup you can't, so we would rather win in the cup.
"But we are getting a bit selfish now and would like to win both."