The short answer to the question in the title of this blog post is 301 is much cheaper. 304 Stainless steel has more Chromium, so it will better match your appliances and more Nickel, which hardens the steel and make the luster last longer. Sinks made with 301 Stainless Steel or lesser grades will not match your appliances out of the box. Some manufacturers put a coating on the sink to mimic the luster of 301. If a coating is applied, it will quickly wear off and become dull and grey. Sinks with a lower Nickel content will age faster.
Here is a link to a great article with a lot more detail on the differences between 304 Stainless Steel and 301 Stainless Steel.