The Mughal Empire had a much lasting impact on the History of India than the Marathas. There are many reasons for this.
The Mughals were truly Empire builders. They actively concentrated on different aspects of Empire building like conquering territory, consolidation of the Empire, reorganisation of revenue system, extraction and distribution of surplus, revamping the administration and economy etc. The Marathas paid scant attention to these aspects and after the time of Shivaji ( which historically speaking doesn’t count as the period of Maratha Empire) the consolidation of conquered territory and other aspects that make an Empire lasting was not given attention. This is why while the Mughal Empire lasted more that 200 years, Maratha Empire faded as fast as it appeared in the Historical Canvas of India.
Dr. Balaji Viswanathan (பாலாஜி விஸ்வநாதன்) has misintrepreted the influence of Marathas on the history of modern India (whereas he is spot on about contemporary India). It is a mistake many Nationalist historians have also made. The Mughals were a great inspiration to many Muslims as well as Hindus in India. It was in fact with the beginning of communal history writing which began with James Mill, who periodised Indian History into Hindu, Muslim and British periods that Mughal Empire took a backseat in the minds of many Indians. Consider the 1857 Revolt. The first thing the rebels (which constituted both Hindus and Muslims) did was to capture Delhi and seek the support of Bahadur Shah (last Mughal King). No one even remembered the Marathas. The Mughal Empire as a Pan Indian entity was very strong in the Indian Pscyche and this incident demonstrates it. Delhi was the epi-centre of the revolt and not Pune. This was because Pune of the Peshwas was not as majestic in the Indian mind as was Delhi of the Mughals.
The Mughal influence on Indian art, literature, sculpture, architecture, painting, language etc, is unparalleled. The Marathas can lay no claim to that kind of influence on Indian history. And this was not a religious influence. Consider the miniature paintings of Rajasthan or the Pahadi paintings. Consider the evolution of Dance forms like Kathak. Or the architectural styles that evolved during the period. Mughal influence can be seen in every aspect of Indian life, without religious colour.
Most of the modern ideas that British introduced were carry overs from the Mughal legacy. The revenue organisation, monetary system, justice system, administrative system etc were all based on the Mughal system initially. It was only later that the British started to evolve their own models. Even then there was no complete break from the former systems. Marathas did not even enter the picture.
It would be unjust to think that Maratha influence was more on the Indian History based on a few incidents like the Shivaji festival conducted by Tilak or Ganesh festivals. These were mostly confined to Maharashtra (home state of Tilak) and in fact had a polarising effect on the Freedom Movement. Evidence can be seen for this on the revolutionary movement of the 1920’s and 30’s where the revolutionaries under Bhagath Singh and Surya Sen completely shunned such uses of religious or Regional symbols. This meant a much more inclusive participation.
Another aspect that needs to understood is the fact that the Maratha state in fact adopted most of the Mughal Systems as its own. Even though they did adopt different names for everything, their administration and economic system was largely based on the Mughal model.
So, in short, Mughal Empire undoubtedly was more influential in the history of India. And it continues to influence us in many things. From Urdu to Biriyani, from Rupee to Roads, Mughal influence can be seen in many aspects of Indian Life.