A few observations:
Classics is an enormously rewarding area of study - if you have the aptitude for the languages, are interested in the material and are willing to do the work. Classics helps you understand Western history, literature, art, philosophy and politics more deeply and enriches your life experience.
That aside, I think the practical applications of Latin are generally overstated. It might help you a bit with vocabulary, or in learning Romance languages later. There is one area where it can be quite helpful, though, which is getting into an elite college.
Harvard and its peers all have Classics departments which don’t attract enough students (although Harvard has less trouble than most), in these days when there are more STEM majors than ever. As an illustration of how you can distinguish yourself, about 3,000 people take the SAT II Latin test each year, and about 150 of them score 800 (see here to understand how comparatively rare an 800 in Latin is: https://secure-media.collegeboard.org/digitalServices/pdf/sat/sat-percentile-ranks-subject-tests-2015.pdf). If you’re one of them, the admissions offices will notice, particularly if it looks like you might go on to be a Classics major and ideally do further work in the field.
Chinese has infinitely more “practical” use, but you need to bear in mind that a native English speaker (as you seem to be) can study it for many years before achieving fluency or being able to read a newspaper (see this classic article on why: http://pinyin.info/readings/texts/moser.html). You really need to live in a Chinese-speaking country for a while to get to a level where you can have extended conversations on a wide range of topics. If that’s something you think you might want to do, particularly if you might use Chinese in your career, then getting started as early as possible might be better for you.
Bottom line: both can be rewarding and useful, but in very different ways, and you’ll have to work hard to get the benefits, whichever you choose.