Is calculus or statistics more useful for non-science/ math majors? Why?

This is an excellent question to ask, and it happens to be one of those questions where the answer is actually very clear. Statistics wins. Whether you see yourself in a career based in the humanities, law, or business, statistics will give you essential tools for getting along in our modern society. It's like learning civics. It's something that everybody needs.
I say this as someone who has great respect for the power and importance of calculus. Calculus is the intellectual gateway for understanding how, in quantitative terms, systems change. It's essential in physics and engineering, and important for natural scientists in many other fields. It's also -- like music theory, logic, geometry, and other abstract studies -- great stuff to know about.
If it's a question of either/ or, though, the answer is statistics. Statistics is crucial for becoming an intelligent consumer of information in the modern world. 
When you lack training in statistics, you're an easier target for misinformation. People are constantly making claims about numbers that affect your everyday life, local community, workplace, and nation. Statistics helps you make sense of these claims. 
It also helps you put important everyday problems to the test. Is your school, workplace, or government showing favoritism towards certain people? Statistics gives you the tools to test whether certain things happen more than they ought to happen, under the assumption that everyone is being treated equally. It allows you to identify circumstances that seem too good to be true (i.e., really unlikely). It allows you to set up objective tests for whether, say, your company really is selling more widgets since you began the new ad campaign, or whether claims about the latest unemployment statistics really show what a politician says they show, or whether it really is all that damning that a defendant's DNA test matched a forensic sample.
Statistics also helps you put your own, personal data in perspective. How good or bad was that last test score of yours? If you take a medical test, what are the chances that you'll be incorrectly identified as suffering from the disease? What are the chances that you'll be given a false negative -- a result that incorrectly concludes you are healthy when you actually have the disease in question? In serious medical situations, understanding statistics can protect you from dangerous misunderstandings. It can keep you from panicking unnecessarily or being overconfident about the results of a test.
Being familiar with statistics will also help you understand how science works. Virtually all experimental science that affects your everyday life depends on statistical analysis. Scientists don’t just give one group a green pill, another a placebo, and then decide that the green pill is effective because more of the people who took the green pill got better. Scientists have to analyze their results statistically in order to decide if the difference between groups was large enough to conclude that the green pill really made a difference.
What does it mean when scientists say they found a "statistically significant" difference? Sometimes, it means very little in the real world because the effect itself was actually very small. Studying statistics will help you be sensitive to these things and empower you to be a more active consumer of the latest scientific claims.
Finally, I want to address the question of intellectual stimulation. You might think statistics sounds like a lot of practical but boring stuff -- not appealing to somebody who loves to think about deep ideas. There are some intriguing things to think about in your introductory stats class, though. You'll learn some theory about probability, which has interesting philosophical implications.
http://www-math.mit.edu/%7Edjk/calculus_beginners/chapter01/section02.html