They are both great papers, but the former has an advantage over the latter: nytimes.com recognized that I am viewing it on a mobile device and switches the page to make it readable to me. So does WSJ.com and the GlobeAndMail.com. Not to mention talkingpointsmemo.com.
I think any major news or business magazine or newspaper needs to do this ASAP or lose readers in the process.
Smart People I Know 
And the Washington Post has one of the most poorly laid out online media sites. Cluttered, hard-to-navigate, ugly.
Their goal seems to be to pack as much text and links as possible without thought to design or functionality or graphic appearance.