Both India and China are large countries that gave rise to a diversity of cultures. In addition, as neighbours for 5000 years, a lot of culture has been shared and transferred between the two. As such, the cultures are very similar in a lot of ways. One could write books on this topic, so it's difficult to write a short answer.
Among the similarities include:
1. Significance of the family unit
2. Attitudes toward teachers, education and child upbringing
3. Both are superstitious cultures (for example, superstitions surrounding when one can cut hair, cleaning the house before holidays, etc.)
4. Belief in luck
5. Lunisolar calendar systems (India has several traditional calendars, some of which are lunisolar)
6. Associations of colours with ideas (red being one of the most auspicious, white being the colour of mourning and death in both Indian and Chinese tradition)
7. Hosts and guests and how they traditionally receive each other
8. Music based on pentatonic scales (India and China both each have many other styles, but both make extensive use of pentatonic scales. In particular the popular Indian ragam mohanam is exactly identical to the Chinese pentatonic scale)
9. Philosophical and religious ideas (reincarnation, karma, various deities) especially with Buddhist Chinese -- mind you there are hundreds of millions of Chinese around the world who are worshipping an Indian guy, which shows the extent to which the countries have shared/imposed/propagated/traded ideas with each other
10. Idol worship
11. 5 elements, but 2 of them differ (China: Wood, Water, Earth, Metal, Fire; India: Earth, Water, Fire, Air, Ether)
12. Beliefs in traditional medicine
13. Tea cultivation -- both India and China have been doing it for so long, nobody has the slightest clue who had it first
14. Rice cultivation
15. Food -- you might wonder why I list this as a similarity, but many people in the West see only a small fraction of Indian cuisines and a small fraction of Chinese cuisines. In reality the foods take a more gradual transition from Indian cities to Chinese cities, and foods that came from outside became common to both (naan, for example, which is common to both northern India and western China, uncommon in both southern India and eastern China). Then there are the raw ingredients. Indian and Chinese cuisines have a lot of similarities in the vegetables used, and even spices to some degree. It's the way they're used and mixed, and the cooking methods that are so vastly different that one might not recognise that there are even similarities in what's stocked in the kitchen. South Indians and Chinese regularly shop at each others' grocery stores and markets in southeast Asia.
Among the differences:
1. Language structure and grammar is different, even though Indian and Chinese languages have both imported a little vocabulary from each other
2. Attitudes in a group, the amount of individualism one expresses directly, and when it is appropriate to be expressive in a social context
3. Conflict resolution
4. Attitudes regarding embarrassment and losing/maintaining face
5. Directness vs. indirectness in personal expression
6. Gestures of indication (for example, yes/no/happiness/sadness) differ between the two
7. Methods in traditional medicine
8. Chopsticks vs. hands for eating
9. Soy cultivation, which India has done for several hundred years but it never caught on in Indian cuisine as much as it did in China
10. Cooking methods, combinations and seasonings used in food differ greatly
11.Musical instruments -- except if you consider western China and northern India which have a number of similar instruments
12. Festivals and holidays and their religious/cultural significance
13. Literary and artistic traditions
14. Pop culture divides the countries much more than traditional culture
15. Zodiac systems (Hindu astrology has signs that are more similar to Greek astrology and based on the time within a year; it does not have a 12-year or 60-year cycle like the Chinese system)
This list could go on forever -- one could write books about this subject.
