Stanford is the better university by far but there are some serious reasons for choosing Columbia. One is the networking angle. If your career is going to be in the Northweast and Europe then the connections you make in New York (at Columbia and through your interactions with others in New York) are more likely to be around you throughout your life. I would look at the geographic distribution of graduates from Stanford versus Columbia to see if this off-the-cuff thought is accurate.
I wouldn't put any weight in the "I can do a semester at Columbia" bit. Are you really going to travel all the way to New York for a semester to study? What a pain in the neck! Travel to New York for a paid externship OK but study? I can see someone paying the money to travel if they are moving up tier-wise to study but not going from Stanford to Columbia to study. Wasted money in my opinion.
Another angle is your summer work. More likely the appropriate jobs will be in DC and New York - easier to hunt them down from Columbia than Stanford. Easier to get to them and interview for them from Columbia than Stanford
In terms of personal relationships - more likely to meet attractive like-minded people in Columbia and New York than at Stanford unless you like dating nerds
Ivy power - when it doubt go Ivy for the coolness factor - Stanford is only cool if you are in the tech business, IP and venture capital...which comes back to the networking thing again. Which school offers the better networking opportunities for your intended field of study.
I personally think that Stanford Law (and Stanford in general) is very corporate-oriented. Almost as if the Law program is linked with the business school. I think this is because the University is almost orienting itself as a new venture incubator and all the departments are having a hand in that. This makes good business sense, and helps students get great positions, but I wonder how the academics are being affected by this.
Anyway, those are my two cents. I think your choice is one of optimization since you can't go wrong at either school. You are at the point of choosing which is more optimal for achieving your goals. I think if you are sure of your goals, as stated, then Columia otherwise Stanford may be the better choice. (Remember, the prestige of Stanford amongst the public is more for its tech-related programs than their law school while everyone associates Ivy with good law and business programs, whether they are or not!).