New York is 3 times Chicago's population but because surrounding states have effective gun control laws, New York has fewer murders than Chicago.
Size of Chicago's population vs size of New York City's is not that relevant to the discussion of murder in Chicago. When comparing ethnicity, New York has about 8 million Jewish individuals out a total count of about 10 million folks. In Chicago, the Jewish population is a strict minority.
From about 1960 to the present, the population of Chicago has changed from being a very Polish-American City ( one million +) to one, that consists of 1/3 Hispanic, 1/3 Black and 1/3 White. Chicago is in a perpetual state of migration, with City folks moving ( all the time) to the suburbs, to other Cities and even countries.
Besides this racial/ethnic population flux, there has been a steady decline in the number of Catholic Churchs and schools on the SouthSide and else where in the City. From an educational perspective, the Catholic Schools offered an excellent education for all kids, whether they could pay tuition or not. Also, whether they were Catholic or not... These schools are now gone. What's left are primarily the Public schools and the Charter schools.
In many parts of the Southside, empty Catholic Churchs and schools lay in ruin and decay...Even in several previous parts of the City formerly populated primarily by Jewish residents, Temples either lay empty, or have been converted to Black Churchs or even an Islamic Centers.
Many of the problems of inner City Chicago, stem from poverty, high unemployment, lack of strong educational opportunities, absence of fathers in the home, and the increasing number of single mother homes, often with the mother no-where in sight with the grandmother taking on the responsibilities of both father and mother.
An so on...As you can see ( hopefully) the problem of murder in Chicago is due to a multitude of things, besides whether a gun comes from Indiana, Iowa, NY or outer-space. Or if the gun is registered.
If guns weren't the cause of the murders, knives ( as often they are ) would be.