Of these two black sheep consoles, both of which were something of a commercial stumble for their makers, which do you think is better, and why?

The PS3 is a fantastic multimedia device. I loved the ability to load videos and pics onto the system and all of the file types it supported and having a BD player was great.

But regarding the library of games born on each console, then definitely the Gamecube. Even against the Playstation 2, exclusives like Metroid Prime, Wind Waker, REmake, Smash Melee, Eternal Darkness, F-Zero GX, Animal Crossing, Pikmin 1&2, Rogue Leader and Thousand Year Door kept me from caring much about Sony's console that gen. Add to that the predominant version of RE4 and other great multiplats like Viewtiful Joe, Splinter Cell and Soul Calibur 2 make Gamecube one of my favorite consoles of all time. Oh, and Twilight Princess... always forget that one. The only big missteps for me was Mario (Sunshine and Kart). I loved a lot of the games during the 7th gen too, particularly the mighty Bioshock, but except for Uncharted 2 (and 3 to some extent) and Metal Gear Solid 4, there wasn't a whole lot that stood out to me that I could only get on the PS3.

As a pure games machine, the Cube wins this one pretty easily for me.

That's tough, The PS2 was my first non Nintendo system but I still leaned Nintendo at that time so the GameCube was my system of choice that generation. I really enjoyed the PlayStation 3 and liked it more than the Wii that generation. I loved both systems, if the question was GameCube vs PS2 it would be a no brainier GameCube for me, but when it comes down to the PS3 vs GameCube I would slightly lean GameCube but could make an argument for PS3 just as easily.

I'm a graphics whore and liked better games with good graphics. The PS3, no doubt, makes my cut. There were a lot of fun indie games on the system.

The Gamecube has the home console pokemon games, so it wins for me. Though it's a close call if we take into account the original fat PS3 version, backwards compatibility with PS1 and PS2 means a massive library.

GameCube is where Tales of Symphonia originally released.

PS3 had a remastered version... which included the sequel *shudders*

The choice is clear.

RPG wise....

Gamecube:
Paper Mario TTYD , Skies of Arcadia Legends, FF Crystal chronicles.

vs

PS3:
Legend of Heroes : Trails of Cold Steel series + Atelier Dusk series + Ar NoSurge : Ode to an unborn star + Fairy Fencer F + Final Fantasy XIII + XIII-2 + Resonance of Fate + Dragon Age II + Dragon Age Origins / Inqusition + Elder Scrolls Skyrim (+dawnguard) + Mass Effect series + Final Fanyasy X+X-2 HD remasater + Fallout 3 + Star Ocean the last hope + The Witcher II + Ni No Kuni : Wrath of the white witch + .... and on and on.

The amount of rpgs on the PS3 is like 20-30 times that of the Gamecubes, and most of them are higher quality.
As much as I love Paper Mario TTYD, it doesnt counter all the others the PS3 had.

It's gotta be the PS3. It had some great exclusives, mgs4, Uncharted 2 and the last of us were some of my favourite games ever. And there were so many great 3rd party games like GTA 4 and 5, Red dead redemption, tomb raider, elder scrolls, sleeping dogs, resident evil 5, Yakuza 3,4 and 5. I owned around 100 games on PS3 and most of them were AAA games. I forgot about all the assassin's Creed games played all of them and loved them all

Pretty sure Witcher 2 wasn't on PS3, just PC and 360.

Gamecube is what I grew up with. Some of my all time favorite games are on the system.
Imo it has one the best exclusive libraries ever. I've used my Wii more often to play Gamecube games than actual Wii games.