I'd offer two (rather inter-related) contributing factors as to why the indigenous polities like the Marathas or the Sikhs failed in the face of the British:

1. Political fragmentation

2. Poor leadership on the battlefield.

Political Fragmentation

When the British faced off against the Marathas, they weren't facing a coherent state with a unified leadership, rather they were confronting an agglomeration of powerful and independent Sardars such as the Sindhias, Holkars and Bhonsles; these sardars were often at odds with each other as they were with the British thus the rather formidable Yeswant Rao Holkar sat by in 1803 as the Sindhias, Bhonsles and British fought hoping to exploit the weakened combatants; after the British were done with Sindhias and Bhonsles, they turned on Holkar and neutralized him as well. When the British confronted the Sikhs in 1845, the Sikh state was in shambles as it hadn't filled the power vacuum left by the death of the great Ranjit Singh. Ranjit Singh's formidable Khalsa (army) had degenerated into praetorianism and killed several of his successors, looted the country with impunity and threatened the royal court for pay raises. While power nominally rested with the Maharaja and wazir, the real power lay in the elected councils of the Khalsa (the panchayats). Meanwhile, feudatories such as Gulab Singh of Jammu were engaging in their own ambitious state building enterprises (such as invading Tibet) and were plotting with the British. In short, however powerful the armies were of the Sikhs or Marathas, they were wielded inefficiently due to political fragmentation. The British could form a coherent strategy while their opponents, with their manifold and confliciting interests, could not.

Poor Leadership

Both the Marathas and Sikhs engaged the services of European mercenaries to modernize their forces in line with Europe. Mahadaji Sindhia, for instance, hired the services of Benoit de Boigne in 1784. de Boigne had formerly served with the Irish Brigade in the French army, then a Greek battalion in the Russian army and finally a native unit of the British East India Company; his career with the company was cut short due to an affair with an officer's wife and so he switched allegiances to the Marathas.de Boigne organized the Sindhia's army along British lines and he hired a Scottish mercenary named George Sangster to oversee the Maratha gun foundries. In addition, European mercenaries (predominantly British or Anglo-Indian) also served as mid-level and junior officers in Sindhia's army and they did excellent work. The quality of the Sindhia army was, by the judgment of one rather obscure British officer called Arthur Wellesley, on par with the EIC's own troops and this is corroborated by accounts of other officers as well. Wellesley was particularly wary of the Maratha artillery which was patterned after the French. Unfortunately, mercenaries tended to be swayed by money and the EIC exploited this weakness wholeheartedly by buying off many of Sindhia's officers with positions and generous salaries. Daulatrao Sindhia (Mahadaji's nephew and successor) completed their work by ordering the remaining British officers to be sequestered or fired. The army that confronted Arthur Wellesley at the climactic battle of Assaye (1803) was one stripped of its most veteran officers and barely led (in fact, the commander of the Maratha army, Pohlman was not even present on the battlefield!) and yet the battle was a hard-fought 'near run thing'.

It should be noted that only a small portion of the Maratha army was composed of this westernized infantry and artillery. A good portion of the army at Assaye and other battles were pindaris, light horsemen good for looting and interdicting supply lines but little else. They simply watched at Assaye as the Maratha infantry clashed with the EIC troops and fled upon Wellesley's triumph. So numbers don't mean much unless they are brought to bear in battle - spectators don't count!

Much like the Sindhias, Ranjit Singh also employed European mercenaries of various backgrounds, including EIC deserters and French veterans of the Napoleonic Wars. Ranjit Singh also took into account the desertion of Sindhia's mercenaries and attempted to counter this by creating an indigenous Sikh officer corps and fostering loyalty among his European mercenaries through marriage and oaths. Unfortunately, upon his death in 1839, the European mercenaries were removed by Sikh nobility and indigenous leadership proved lacking or treasonous. The Khalsa, as mentioned, had become a dangerous political force in Sikh politics and was actively threatening the royal family and court for higher pay. The Anglo-Sikh War was a welcome respite for the court as it would either distract or destroy the Khalsa. Military commanders tied to the royal court such as Tej Singh and Lal Singh were working at cross purposes with the Khalsa's regimental commanders and regularly communicating with the EIC with the intent of greatly curtailing the Khalsa (they can't threaten you if they all died in battle, right?) and furthering their own amibitions. This clash in motivations would prove devastating to the Sikh war effort. Perhaps the best demonstration of this is the Battle of Ferozeshah, where Tej and Lal Singh dithered and ordered a premature withdrawal, thereby preventing the destruction of the badly battered EIC army (and upon the conclusion of the Anglo-Sikh War, who should become Wazir and Commander-in-Chief respectively but Lal and Tej Singh?) Even the best equipped army is useless if the government leadership is actively conspiring with the enemy.

Sources:

1. Singh, Bawa Satinder. Raja Gulab Singh's Role in the First Anglo-Sikh War. Modern Asian Studies, 5, 1971, pp. 35-59.

2. Cooper, Randolf G.S. Wellington and the Marathas in 1803. The International History Review, 11, 1989, pp. 31-38

3. Roy, Kaushik Military Synthesis in South Asia: Armies, Warfare and Indian Society, c. 1740-1849, The Journal of Military History, 69, 2005, pp. 651-690

4. Barua, Pradeep Military Developments in India, 1750-1850. The Journal of Military History, 58, 1994, pp. 599-616

5. Cooper, Randolf G.S. The Anglo-Maratha Campaigns and the Contest for India: The Struggle for Control of the South Asian Military Economy. Cambridge University Press, 2003.

6. Barua, Pradeep. The State at War in South Asia. University of Nebraska Press, 2005.