It's really quite rare that these two holidays can actually coincide; it has only happened about 3 times since 1900, and probably won't happen again for a few decades! There's been quite a dilemma about which should be celebrated here in Singapore. The Chinese people have been wondering about whether to spend time with their partners or with their families, whether love and romance is more important than family bonding etc. There's little in common between these two events: besides the plentiful use of red, there is also the dinner(family reunion or date), and the loss of money(given away or spent)!
Other than that, they are very VERY different. The receiving party in V-Day is usually the girl, whereas for CNY both give and receive. On V-Day items given include chocolates, flowers, bracelets etc, while CNY usually just involves oranges and red packets. V-Day celebrations are usually most evident at night with all the romantic dinner dates, while the CNY festive mood is present before and after dark. This is why the Chinese usually have to pick just one to go along with, since each event has totally contrasting demands from the person!
Another problem is weddings; although it sounds like a good idea to wed on Valentine's Day, the Chinese believe it to be inauspicious to have a wedding on the first day of the New Year, so Chinese couples have a tough decision to make! I think if they really cannot wed on Feb 14, maybe do it the day after(Feb 15). It would probably make the wedding anniversary easier to remember too...
Because of this clash, some people have been actually coming up with ways to merge these two days together, for example giving the two events a single name like ValenTiger's Day! Others have been coming up with artwork that mashes elements from both events together:
...There's probably lots more mashups like these, but I won't spend that much effort trying to find more...
Oh right! A few MAJOR problems with this holiday clash is that usually couples would go out for a dinner date on V-Day, but then restaurants/food stalls might be closed because of Chinese New Year! Also, most shops would be closed too, so shopping might be more limited too. This affects ALL couples, not just the Chinese. At least you can still watch movies: there happens to be movies for BOTH CNY AND V-DAY! Well obviously there's the movie Valentine's Day, and I managed to find the Singapore showtimes here! As for the CNY movies, there are several possible movies actually, including 72 Tenants of Prosperity (72家租客). Maybe you could go and watch them now? Or after dinner?
Whichever way you want to celebrate, just remember to enjoy yourself! For all the Chinese people, it would be best to regard BOTH your loved one and your relatives as of equal importance. Don't skip the reunion, but don't neglect your partner either; maybe have the reunion dinner on the eve, then the dinner date on V-Day, when most of the family visiting would have been done with.
So... Happy ValenTiger's Day! :P