If this were a comparision between India and Pakistan, I've seen quite a bit of India. I stay there for a few weeks every year. I will try to be as unbiased as possible from a common man's perspective.
Indian institutions are as corrupt as Pakistani ones. Of the few times I've been stopped by traffic police in India, I've always been let off by giving a small favour. As a matter of fact, all government institutions which I have come in contact with including the CID and immigration officers are easy to buy. We have the same problem in Pakistan. It is hard to decide which side is better at it but since I've not worked or studied in India I can not comment from experience. However, friends and cousins confidently flaunt their skills at their money doing any work. It may as well be easier to bribe in India.
This maybe a no-brainer but Mumbai city feels a lot safer than Karachi. Karachi at times feels like a war zone. Today, a major party's deputy leader was murdered in London (probably murdered by his own because of differences with the leader) and Karachi was at a standstill. All markets and even petrol pumps were closed.
For entertainment, I'd think both cities would be at par with the absence of any decent cinemas in Karachi. As far as boutiques, and restaurants are concerned, both have their unique styles. Mumbai does feel a bit bigger with many more hotels and tourists to be seen. The security situation over the past few decades have really hurt us.
The roads here are definately better. Much better. Even outside the cities on the motorways and highways I think our roads are better. The Mumbai-Pune expressway is a good road, but it has already started aging. The highways linking Islamabad to Lahore, Peshawar and other cities are in my opinion of a higher standard.
Railways? The Indian railway system is light years ahead. I've never actually been on a Pakistani train but from what I hear they are outdated and even dangerous. The railways minister here said that before boarding a train, pray to God. Such is the situation of the railways here. Indian railways are really good but pale in comparison to U.K, and China. They still feel like a 3rd world system.
I find Karachi, Lahore, Multan and Islamabad much cleaner than the Indian cities I've visited. Mumbai's slums are the worst in the world. Most of the city stinks. Karachi has another problem. Air pollution. The transport mafia is so strong, a ban on black-smoke emitting had to be revoked. But Mumbai is a pain to drive in. Traffic and honking, along with manual laborers pulling carts is a nuisance.
Racism and ethnic tension if prevalent everywhere in both countries. It's a shame really.