"Before long I'll be dead, and you and your brother and your sister and all of her children, all of us dead, all of us rotting underground. It's the family name that lives on. That's all that lives on. Not your personal glory, not your honor... but family."
--
Tywin Lannister is the head of House Lannister, Lord of Casterly Rock, Warden of the West, Lord Paramount of the Westerlands and, currently, the Hand of the King to his grandson, King Joffrey Baratheon. Intelligent, calculating, and ruthless, he is also the richest man in the Seven Kingdoms. His primary concern is his family's legacy.

vs.

"Your meat... is bloody tough!"
--
The Greatjon is the Lord of Last Hearth and a formidable and proud bannerman of House Stark. He is a large, formidable warrior. He is fighting for Robb Stark in the War of the Five Kings. He is not present in the second season and it is assumed he is leading northern forces fighting elsewhere. His role as Robb's chief northern advisor is taken up by Lord Roose Bolton.

Tywin. Easy.

Sorry Greatjon. You never stood a chance.

It doesn't hurt that Tywin is played by my favourite actor on the whole show.

Going with the Warden of the West.

Pity vote for Greatjon even though Tywin is clearly the superior choice.

Spoilers up to AFFC

+

The fact that it took so many Freys and Boltons to overpower him when he was shitfaced drunk during the Red Wedding forever earned him a place in my heart. He threw a table and gave it all he had. And as many people have pointed out on the internet in the past, the Umber sigil is a giant breaking free of chains. I can only hope that foreshadows something amazing in his future, since he is chained up in a basement somewhere. Though it appears they've changed the sigil in the show to just be four chains hooked to a central ring.

To your 2nd para Niney... I had never thought of that... Interesting.

I have not read the books, but I love ever scene Tywin is in. One of my favorites.