None of the responses in here really answer the question well other than being rather vague and general, so I will try and take a stab at this.

There were many, many conflicts that the East India Company fought in India, many of which included joint forces of local allies as well as conflicts against other colonial powers (primarily the French and Dutch) in India. However, since we are looking primarily at the EIC, it seems that we need a proper counterexample whereby the EIC was by far the primary participant in the war for the British. Thus, we will get an example whereby the EIC fought against a powerful Indian adversary-in this case, we will examine the Sikh Empire's Khalsa.

The Khalsa was the Sikh Empire's elite army force. Composed of devout Sikh loyalists alongside other local detachments (including Punjabis, Pashtuns, and the like), over the course of the 19th century it was modernized into a more modern army with a plethora of European advisers, training, and equipment. The Sikh units were equipped with modern firearms and had a large contingent of modern artillery and logistics chain. Most contemporary sources described the Khalsa as being more impressive than the more motley looking British and sepoy forces of the EIC, and after the Anglo-Sikh wars the British employed large numbers of Sikhs in their colonial armies (although some of this had to do with loyalty issues in the wake of the Sepoy Mutiny). Given these assumptions, the idea that this Indian army was, on paper at least, inferior to the EIC troops, is rather silly.

So if it wasn't a matter of military technology or training, what could have led to the decisive British victories that destroyed the Khalsa? Historians generally point to a number of causes-for instance, many Sikh historians point to internal treachery. They point at the leaders of the Khalsa as doing their best to lose the war, due to political reasons (namely that with the death of Ranjit Singh, the former leader of the Sikh Empire, the Khalsa became a major political force that the new government was uncomfortable with). While there is certainly evidence to support this (such as alleged communications between Lal Singh, one of the Sikh generals, and the British), this doesn't entirely explain why the actual Sikh units experienced tactical defeat on the battlefield.

One example is at the Battle of Mukdi, one of the first clashes between Sikh and British troops. While it is true that the Sikh forces were not operating in tandem, rather than allegations of treachery I would suspect that poor communications and coordination played a bigger role in creating a situation whereby much of the Sikh army did not participate in the battle against the EIC forces. However it is important to note that the key clash-Sikh cavalry being routed by a British countercharge-demonstrates a few key points about the differences between Sikh and British troops. Namely, that while the Sikhs may have been good horsemen and individually skilled, they were inferior in their discipline as a unit-the power of cavalry lies not in the individual rider but in the unit's cohesion as a whole to deliver shock action against the target of its charge. In other words, superior British discipline carried the day. Many of the troopers themselves were also Indian, so arguing that the British soldier was somehow inherently superior is a bit much.

What is also important is examining the following campaigns. While the Sikh divisions typically fought valiantly, they did so either in piecemeal or with poor coordination. While this can surely be blamed on incompetent or indifferent commanders, the lack of a system to relieve said commanders or the initiative of other local officers is also a sign of poor communication within the Khalsa's organization. British commanders were also criticized for their mistakes, but unlike the Sikhs' they could relieve failed commanders and appoint new ones that were already familiar with the area and had "usually" been promoted due to merit. Much of the army consisted of light irregular cavalry as well, which while excellent for scouting and raiding are of little use in pitched battle against infantry squares and artillery. This can be seen in the aftermath of the Second Anglo-Sikh war where much of the Sikh army that eventually surrendered was composed of these types of cavalry. The use of these cavalry in Sikh lands is well understandable-Ranjit Singh had used them to deal with the threat of Pashtun Raiders as well as to cover the difficult terrain that would make it more difficult to move massed infantry and artillery (along with their baggage trains)-but they performed less well against British dragoons, line infantry, and rifled artillery.

To summarize, even a modernized Indian army with modern equipment and European advisers ended up losing to the EIC, primarily due to poor communication-which is an organizational issue-and a military structure that was organized to fight the wrong kind of war-whereas the British EIC armies were specifically designed to fight these kinds of low-scale colonial conflicts.