I agree that the steaks at Republic might not pack as much flavor as those at Christopher's, but that is why they serve them with a trio of sauces. I love that green steak sauce mixed with some of the horseradish sauce.
In regards to other foods, the lamb at Republic is definitely better than Christopher's. Also, the drink menu and bar at the Republic are better. Try the Bloody Marys at Republic, my wife's favorite in town and i don't think its on the menu anymore. Both have good soups. Both dessert menus are pretty good although i think some other places in town have better desserts.
In regards to other places in town with good steaks i like the duck at Veritas and they have amazing calamari, but i wouldn't put their steaks with the top two. Others like Maddens i don't think are in the same ballpark. I haven't tried Porters but haven't heard good things either.
Biggest thing is if you want a complete plate with sides and no thought then Christopher's is the place for you, and if you like to make your own plate with sides then Republic is the place to go. This is just my two cents on those restaurants. To each is own.