Mussina didn't have as many opportunities to win games (better opposing pitchers going against him than against glavine, worse offenses in Baltimore giving him lower run support etc), and thus didn't register on the Cy Young voters minds as much.
This may or may not be true, but it's not the real story. Wins-wise, the difference between Moose and Glavine is all about the fact that Glavine started a year younger, pitched a couple years older, and stayed a little bit healthier throughout his career. Mussina won over 50% of his starts in his career; Glavine won under 45%. Moose also pitched more innings per game. He's still a lot of wins and a lot of innings short for the reasons I listed above, but there really is no meaningful metric by which Glavine was a BETTER pitcher than Moose, when he was pitching. Mussina threw more innings per game, won more per game, had a much better WHIP, had a substantively better ERA+. Moose also lost a smaller proportion of his games than Glavine. Glavine has the best single-season WAR of the 2, but his 2nd best is equal to Moose's 4th. In fact, in spite of basically 4 full seasons less career pitching, Moose trumps Glavine in career WAR by over 10%. Moose has a much higher career K rate. A much lower career walk rate. A lower hit rate. And those last 3 things aren't even normalized for the fact that Glavine got to pitch to pitchers his entire career, while Mussina spent his entire career in the AL East.
I don't see how anybody rational can look at the 2 and say that they honestly believe that Glavine was a better pitcher. If you want to say something like "We want a Hall of Fame that includes every pitcher who has won 300 games," fine. Then put Glavine in. But don't pretend you actually think he was a better pitcher. There's no way in hell.