Q: What's the difference?
The left button uses standards compliant DOM methods such as createElement, createTextNode and appendChild to generate the HTML table. The use of these DOM methods guarantees that the function will work in just about every current browser as well as any future browsers. The downside however is that these methods are slow when compared to the alternative approach - that of generating long HTML strings.
Though not standards compliant, this faster version also works in just about every current browser. As such, until the DOM methods have caught up with the alternatives, I would recommend avoiding them unless the tables you plan on generating are consistently small.