I'm not familiar with the Khmer Empire specifically but I can answer generally the question of Indian influence vs Chinese influence on Southeast Asia.

The question of “why India and not China”, not just regarding Champa but the whole of Southeast Asia, has not yet been answered with certainty. We don’t know for sure why so many Southeast Asian rulers from the 5th century onwards adopted Indian religions and a model of state instead of anything else. Records from this period are lacking, and the region has not been studied nearly as much as some other parts of the world.

However, what is considered to be the most likely reason is this: Southeast Asian rulers found that Indian religions, practices and state organisation were useful tools to enhance their own legitimacy. While China also offered such a model, indeed, offered it much earlier than India, Southeast Asian rulers found it threatening and thus rejected it.

China vs India first contact

Available evidence points to very limited Indian contact with Southeast Asia before the 4th century CE. Prior to the 4th century, there are few examples of Indian goods in Southeast Asia, indicating extremely limited trade. Literary evidence for links between India and the lands to its east is sparse. And the level of open-water seafaring technology we know of does not seem indicative of regular voyages from India to Southeast Asia. Indeed, a 1996 summary of maritime archaeological finds from the eastern Indian Ocean noted that

No indigenous Asian ships… have been recovered from an archaeological context west of the Straits of Malacca.

It is only in the 4th century that we see much stronger links between the two regions. Indian religious iconography, Sanskrit terminology and coinage all start appearing around this time.

China, by contrast, was well aware of Southeast Asia and was keen to exploit it. The 2nd century BC Chinese text Huainanzi mentions that the Qin Emperor’s campaigns against what is today northern Vietnam (221-214 BC) were motivated by

… the expected gains from the lands of the Yue with their rhinoceros horns, ivory, kingfisher feathers and pearls.

At the time of the Cham polities’ founding, northern Vietnam was already a Chinese province. Indeed, the first Cham polity, Lam Ap, was founded in 192 CE as a result of a rebellion against Chinese rule.

Thus, when it came to contact, especially with the Cham, the Chinese had the Indians beat by at least 400 years.

Rejection of the Chinese model

While there was certainly trade going on between Chinese and Southeast Asian traders, the most visible contact between the two regions was China’s subjugation of northern Vietnam by force, and its subsequent enforcement of its rule for roughly 1,000 years. In this part of Southeast Asia, the Chinese model of state and culture was dominant, but was associated with a conqueror. To make matters worse, the Chinese view of the world placed the emperor of China at the centre and labelled all cultures outside China “barbarians”, including the Vietnamese before Chinese culture had been enforced.

This was not attractive at all to the rulers of Southeast Asia looking to strengthen their position. Accepting that the only way out of savagery was to submit to China was a nonstarter.

The Cham especially did not have much love for the Chinese. In 605, the Chinese general Liu Fang invaded and sacked the Cham capital. Such outbreaks of war only served to turn Southeast Asian rulers off the Chinese model.

Adoption of convenient bits of the Indian model

Early scholarship on the “Indianisation” of Southeast Asia held that Southeast Asia was simply a collection of primitive cultures that adopted Indian culture because of its obvious superiority. In this version of history, the mere fact that Indians were able to reach Southeast Asia via the monsoon winds was enough to cause the adoption of their culture.

This has long since been discredited. In the 4th century, when we start to see evidence of stronger links between India (and note that India at this time is not one unified country) and Southeast Asia, sophisticated polities already existed across Southeast Asia. These polities had their own methods of running themselves and had not adopted the “China model” despite it being around for hundreds of years.

Newer scholarship examines not just the supply of external culture but also the recipients of that culture, and theorises that the Southeast Asian rulers adopted specific parts of Indian culture to legitimise their power.

The idea of merit accumulated over lifetimes, for example, was very popular among Southeast Asian rulers. If everyone is born into a role in society because of the merit accumulated in a past life, the mere act of someone becoming king implies he has done something in a past lifetime to deserve it. And if you were born a peasant, don’t get any ideas about rebelling, because a peasant is what you’re supposed to be because of what you did in your past life.

Large structures like temples were built. Locally issued coinage, based on Indian iconography and weight standards, has been found on mainland Southeast Asia. These probably served as visible signs of rulers’ power, or helped increase control over aspects of life such as the economy.

At the same time, we see other aspects of Indian culture, such as the caste system, not being adopted. We think this was a conscious decision, either because these would not fit into existing social orders, or because rulers did not see them as advantageous.

There is no evidence that Indian culture was being enforced through conquest, and we think that because it was so non-threatening, Southeast Asian rulers were more open to it. Also because it was not being “enforced”, local rulers were able to pick and choose the aspects that appealed to them, thus leading to polities that had a syncretic culture, rather than something imported wholesale from India.

Thus, it could be said that a big reason for adoption of Indian culture instead of Chinese culture was, ironically, that India was so much further away.