We USED to match when we had our Green and Gold colors on our site, but since we swapped up to a darker color it no longer matches. Since our business cards POP however, we will likely continue with the same color scheme and layout on our cards. The important part (as repeated here) is the logo to remain consistent so there's no scratching of the head as to whether they reached the right place or not.
Beyond that, changing up the card is good for finding what works. We get compliments regularly on how our card is designed, so it's not likely that we'll change in the near future.
Personally - I love experimenting with cards, banners, brochures and layouts to see what works and doesn't work. Different markets have different desires. We also have different cards for different markets.
Nothing wrong with a little change - just be sure you're not wasting inventory/funds
