Polgar - Bareev
Judith Polgar always plays 1.e4. Bareev plays the French or the Caro-Kann.
Against the French Polgar always plays the main line with 1.e4 e6 2.d4 d5 3.Nc3. Here Bareev usually plays the Classical French with 3..Nf6, and sometimes 3..dxe4. After 3..Nf6 Polgar plays 4.Bg5, which Bareev answers with 4..dxe4 anyway.
Both player's opening repertoire here is quite fixed, and hence they have already played quite a number of games with this line.
Against the Caro-Kann Polgar plays both the Panov attack with 3.cxd5 and the main line with 3.Nc3.
Against the main line Bareev usually replies 3..dxe4 4.Nxe4 Bf5. This line was considered so super solid a decade ago or so, that many top players played the advance variation (3.e5), but since then there have been found many interesting ways to play the main line.
My guess is that while Polgar has played the Panov attack recently, she will actually prepare the main line Caro-Kann for this match, but that we won't find out because Bareev will stick to his French.
Bareev - Polgar
Bareev is a 1.d4 player. He sometimes plays 1.c4 or 1.Nf3, but to see him playing 1.e4 would be a huge surprise.
Judith Polgar traditionally played the King's Indian, but recently has relied more on the solid Nimzo/Queen's Indian, as so many other top players. I think in a match she will use the King's Indian only if she is behind in the score.
Bareev is playing the Nimzo Indian with 4.Qc2 a lot, where we could expect to see the main line with 4..O-O 5.a3 Bxc3 6.Qxc3 b6 7.Bg5. Here 7..Bb7 is the main line, but 7..Ba6 is also interesting.
Of course I would like to see Judith Polgar in a world championship final again, hoping she would do better than the last time. But Bareev is a very good player, too - I think this match can see a lot of decided games but still go to the tie breaks. I sure am looking forward to this one.