Okami was actually the game that killed Twilight Princess for me.
When I first started playing, it was apparent right away there were similarities. Wolf? Check. Smart Talking side-kick? Check. Cursed land? Checker there as well. (And remember, Okami had been in development for a long time, and had most of these aspects in place well before Twilight princess had)
So when I played Twilight princess I was pretty let down. It always felt like the events in Okami were affecting the people. Big cities, small towns, little houses in the middle of nowhere- you name it and they were all in need of help. The very fact that Ammy needed to gain the "trust" of the people again who had long forgotten her and the other deities ensured that the game needed that emotional connnection with the people. And it worked wonderfully.
The Twilight realm/tears of light quests never really felt like it was affecting anyone but maybe Midna and Link. The -only- time I ever felt bad for any of the characters in that game was when I looked down at Zoras Domain and saw them all frozen. Okami had tons of those moments, and very often they got extremely personal.
Okami did a great job of balancing when to be funny and when to let the emotional tone of a cut scene run. The game had a goofy, lightheartedness about it that was always around the corner when you needed it.
Those all all very important characteristics that I look for in a Zelda game, and Twilight princess didn't bring much of them to the table. After playing Okami, it seemed heartless almost.
Okami is more than a mere clone- it used formula we know and love just as well as Nintendo and came into it's own as well. I would not hesitate for a moment to say the series (as of late, at least with the exception of Spirit Tracks) has proven it can out-Zelda the Zelda series.
It is only fair to mention that Okami only has two games to the series name, though I hope with the adition of Okamiden that the series will continue to grow. And while I'm not the biggest fan of Twilight Princess, I love Zelda at it's finest. OoT is my favorite game of all time and others like WW and Spirit Tracks, and Majoras Mask are ranked very high up as well.
So I voted for BOTH. 8D