it's hard to compare the 3 because of what they offered. xbox and ps2 had something in common that was quite the attracttion that the gamecube did not offer. dvd playback! when the dvd was introduced, it was an included feature of the ps2 and xbox. since ps2 and xbox both offered the feature, it was an extra bonus for buyers to look at these two options and forget about the other brands that did not offer the feature.
also, remember, the ps2 also offered something the gamecube did not offer, backward compatability. so now you have a system that can play dvd movies, ps1, ps2 and cd music all for 300 [299.99] compared to the gamecube that can only play gamecube games all for 200 [199.99]. so when you compared the two, you lean towards the ps2 as it offers the best bang for your buck. the budget dvd player at the time was about 100-120. so if you took out 300-100, you get 200. and remember that the ps1 was also being sold and was for sale at 100, 200-100, you get 100. so you only paided 100 for a new ps2 system as compared to a gamecube which sold for twice as much.
you don't see this effect with the ps3 because no one really cares for blu-ray and hd. the dvd is a media that is more then adequate for the average consumer as of now. in addition, you have consumers who don't necessarily care about high definition, so the extra spending of a blu-ray player is useless.
what would be a great comparison would be the gamecube and the dreamcast. the dreamcast lived only for two years and you compare the gamecubes sales for two years from release and compare the two systems. if the dreamcast out sold the gamecube, then the gamecube wasn't that successful.