As someone who has his whole family in Karachi, but lived in Islamabad growing up, & visited Karachi almost twice a year during those times; I would say Karachi is a huge, bustling, flashier, glamorous, trendy city. I think many people would prefer Karachi to Islamabad and Lahore, but I personally fancy Islamabad over every city. There is a lot of active social life in Islamabad once you get to know a lot of people. It's close to the northern areas, Lahore is less than 4 hours away from it.
Karachi in my opinion is not meant for everyone, it is the survival of the fittest: life is too fast there, & there is a greater disparity of wealth there as compared to Islamabad and Lahore. Mustafa Kamal has done wonders with Karachi, made it an extremely pleasant city with great roads and infrastructure, but personally, its not a city for me; its too crazy. I can take things in Islamabad at my own pace, its big enough to have a great social life (once you get to know the people there), and small enough to think the whole city is like 'your home, your family.' Lahore is a beautiful city stooped in history and its Punjabi culture, again, it has great infrastructure, it has a great social life, and is similar to Karachi; except that it is more historical, but a bit less cosmopolitan than Karachi. But it is also less chaotic than Karachi. It is in between Karachi and Islamabad in terms of social life (a bit less social than Karachi & a lot more than Islamabad), infrastructure wise is very good & similar to Karachi; although Islamabad is always the best in this regard.
I love all these three cities, as well as the other cities of Pakistan. All of them give you a different flavor, have a different character. All of them are developing extremely rapidly, with their expanding infrastructure, yet maintaining their historical ties. I believe it all comes down to personal taste and what you want, because you will get a different flavor where ever you go in Pakistan, it is stooped in diversity and culture.