Since there has never been any objective non-biased study regarding the overall quality of different medical schools in Pakistan, any sort of response you get to this question will be highly biased and subjective.
You can ask for different people's opinions though regarding what they feel are some of the better schools in the country, but you'll find that there is a considerable degree of variance depending on who you ask and whether or not their child or they themselves went to a medical school in Pakistan.
That being said, in my opinion I'd say the Top 4 Government Schools in the country would be something like:
King Edward Medical University (Lahore)
Dow Medical College (Karachi)
Allama Iqbal (Lahore) or Nishtar (Multan) are about the same.
Rawalpindi Medical College (Rawalpindi)
In terms of the Top 4 Private Schools I'd say:
Aga Khan Medical College (Karachi)
Shifa College of Medicine (Islamabad)
Baqai Medical College (Karachi)
Fatima Memorial (Lahore) & Lahore Medical & Dental College (Lahore) are about the same.
Comparing private and government colleges is too hard as they're completely different in everything except for the curriculum they follow. In terms of quality of education most people will tell you that government colleges are better however that seems to be changing as more qualified and strictly regulated private colleges have been established in the last decade. It used to be said that anyone with money could become a doctor via the private medical college route but if you take a look around this forum you'll see that no longer holds true.
Anyways, this is just my opinion but I hope it gives you some idea.
All government schools are EQUALLY hard! KE is NOTHIGN special, it just has a good name due to previous graduates otherwise the books and the teaching and the crappy facilities and stuff are ALLLLL the same! Only thing about KE is that more of the "upper" class students apply there where as in most other govt colleges, its usually lower class rural background.
I have heard KE students are more stuck up towards foreigners, while at other govt colleges they never seen a foreigner before and kinda stare at you and stuff in weird ways!
Shifa would be easier for americans because since they have only 50 students per class, they try to push you along (since their system relies a lot more on your money) and the teachers have more experiences with foreigners making a large percentage of the student body comparitively whereas in govt colleges they treat foreigners just like any other retard student and dont care to help you out much.
Basically comes down to adjusting to the pakistani way of learning and test taking, i you can conquer that your way better at govt college, otherwise easier transition and sailing at a private.