The chinese culture is one of the oldest and flawlessly preserved culture in the world, and same goes for korean culture, people of these countries honor their culture, morals and guidelines.
Chinese culture:
Oldest and perfectly preserved.
Chinese writing: made up of characters containing strokes- complicated process in beginning.
Chinese language is difficult to speak due to tones attached to each word.
Chinese food is a combination of flavors and presentation, eaten by chopsticks.
Tea holds a special place in heart of many people. Slighthly nodds the head while shaking hands as a form of greeting.
Korean culture:
Has a history.
Korean people are generally polite and shy.
Korean language is difficult to learn if we look towards it grammatical side.
Korean people eat with chopsticks made up of several materials.
Loves coffee and tea.
Korean cuisines consist of variety of flavors and methods of preparation.
Bow as a  form of greeting.
South Koreans are quite competitive, which illustrates the reason behinds countrie's success.
Korean art is elaborate and creative.

Differences between the two cultures:
Korean culture is not as ancient as Chinese culture.
Chinese is difficult to learn, read and write while korean is easier to learn and speak but harder to write.
Koreans often use metal chopsticks, but chinese stick to the authentic wood one.
China is diverse country, where korea has 99% koreans.
Koreans likes to take care about their apparence extremely well.

Similarities between the two cultures: 
Both the cultures are well preserved and followed.
Both Languages are difficult to write.
Cuisine consists of variety of foods.
Food is eaten with chopstick.
Rice is a staple food for both the countries.
Both the cultures emphasize on don't work to live but live to work.