The Giro's system is to be stingier with the points (no such thing as a 4th-category climb for them!), and to give massively more points for 1st than for 2nd at each mountain. Any MTF garners a large points selection (3, 2 and 1 for 3rd cat., 5, 3 and 1 for 2nd cat., 10 6 4 and 2 for 1st cat., 15 10 6 4 and 2 for MTFs and 20 15 10 6 4 and 2 for the Cima Coppi).
Now, obviously this doesn't work perfectly; nobody would say Matthew Lloyd was the best climber at this year's Giro, nor would anybody say that Fabian Wegmann was the best climber at the 2004 Giro. But both lost their jerseys to GC contenders with two days left and had to go out and get them back, and both had to get into 7 or 8 breakaways to hoover up enough 3s and 5s to cover the GC men.