Who would win the war btwn India and Pakistan?

India. No second thought about it.

At the outset, let me start off by saying that like the topic under which the OP has been filed (Hypothetical Battles), another Indo - Pak war seems very unlikely in the near future. Also, I am an Indian, so I am obviously biased towards India. However, for the purpose of this answer, I will try to stick more with facts and less with assumption about why I think India would have an upper hand in an India-Pakistan war. 

I do agree with Devika Dwivedi and Sajal Jainin their respective arguments. Additionally, here's what I think will work in India's favor -

1. Military: India has a clearly larger military with access to more defense reserves, budgets and resources. [1] 
   
   
   
2. Economy: A much better, stable and growing economy. India is one of the fastest growing economies in the world in the last decade and has been relatively unaffected by the general economic slowdown worldwide. Their economic stability will help them sustain the cost of war for much longer than Pakistan, if need be.
3. Allies: With the rise of India's economic, political and commercial status, they are way better positioned with their Allies. Pakistan has historically had US and China support them in all three wars fought in 1965, 1971 and 1999. But with the dynamics of US-Pak relations changing drastically after the killing of OBL, clubbed with India strategic partnerships with US in the last five years, I think US will most likely either take a neutral stand or try to get the UN involved to arbitrate. On the other hand, India can always expect support from Russia and Israel in getting appropriate weapons and intel to combat the enemy. Also, India will have a strategic geographic advantage of having an Ally in Afghanistan on the other side of the Pakistan border.
   
   • Note: I'm not sure how relevant this point may be in the context since the OP mentions "if no other country got involved". I'm taking the liberty of assuming that both sides will take strategic, but not military help from their Allies.
4. Strategy: India has a policy of "No First Attack" if the situation ever boils down to a Nuclear War. In such a scenario, India's best bet will be to execute the reported Operation "Cold Start"[2] to neutralize the enemy before they could launch an attack,
5. Governance: India has been a stable democracy pretty much since the independence and partition. Unlike Pakistan, there has never been a tug of war between the Government, Military and the Intelligence Agency about who really runs the country.

In the unlikely scenario of a Nuclear War:According to a report by Natural Resources Defense Council, India apparently has lesser nuclear warheads (about 35) compared to Pakistan (about 48) [3]. It's natural to assume that any nuclear war will lead to a lot of casualties and destruction. That said, both the countries do not have enough nuclear weapons to destroy each other to Ashes. Assuming that the following key geographical targets are attacked in both countries, here's how the overall impact will look.

In such a post nuclear attack scenario, while India would have a slightly higher number of casualties, it will also proportionally wipe out a much larger picture from the Pakistani demographic. If there would be anything left for Pakistan to salvage by the end of it, India would still gain by having the advantage of a much larger military. 

Parting thoughts : 

I object to violence because when it appears to do good, the good is only temporary; the evil it does is permanent."  Mahatma Gandhi