This was because of the massive difference between the political cultures and infrastructure setup of the two countries.
#Part 1
1)Political parties and leaders of the countries-
When both the parties became independent, each got a different type of political leader and party to lead them.
In India, The Indian national congress(INC) party had existed for almost 75 years at the time independence. It had a extremely deeply penetrative pan India presence with almost each district and village having presence of INC party.
The INC had members from all walks of society and all castes, religions and sex. It was an extremely inclusive party. Its political leaders were extremely well known amongst the Indian masses and enjoyed credibility and trust within the Indian public.
INC also had a massive number of leaders waiting in its wing to take up responsibility whenever required. The INC had so many popular and competent leaders all across India that for almost 50 years, INC had no national challenger in elections.
Not to forget, that INC had gandhi too who would often ensure that INC remained connected to commen masses.
Meanwhile, Pakistan had the Muslim league. The Muslim league was dominated by rich Punjabi and Bengali landowners. The leaders of the Muslims league, Jinnah and Liqat Ali Khan failed to decentralise power and never allowed any leader to gain prominence in the party. As a result, the party was extremely over reliant on Leadership of Jinnah to lead them.
Even though Jinnah was popular, The Muslim league party itself did not inspire trust as a party.
So when the death of jinnah took place soon after independence, the party's support and popularity suffered a massive blow. They were dealt another blow when their #2 popular leader Liqat Ali Khan was assassinated in a political rally. Virtually leaderless, the Muslim league was unable to groom any new leaders that could gain credibility and trust of Pakistani public like jinnah did.
2) Jinnah and Nehru
A large part of the fate of the two countries was also determined by their first government.
Nehru and Patel led the first government of Independent India. While Nehru enjoyed massive popularity within the Indian public and was a visionary, he was not experienced in government administration of a massive country like India. In this, he was helped by Sardar Patel(home minister).
Sardar Patel was a veteran of Congress party with a deep insight of governance and administration. The young Nehru learnt the ropes of governance with the help of Patel.
While, Patel died 3 years after independence, Nehru got elected 3 more times and governed India for almost 17 more years until his death.
The long governance of Nehru provided a stabilising force to Indian democracy, allowing to take roots and gain acceptance within Indian public. Also, the 17 years of Nehru rule ensured that no power tussle took place very soon after independence that could have turned ugly.
This could not happen in Pakistan as Jinnah died very soon after Pakistan was created. His number #1 aid liqat Ali Khan was assassinated too after a a few years. These early blows caused young Pakistani democracy to lose its leaders very early before it could gain firm roots in Pakistani society.
to be continued