You are asking yourself should I buy a condominium in New York City?  Well, you should know that New York City property tax is mostly affected by the 1981 Tax Law called S7000A.  See https://en.wikipedia.org/wiki/S7000A. That law created four classes of properties.  Condominiums did not exist in large numbers in 1981.  In fact, parties that were involved in the creation of S7000A actually reported that the law did not consider condominiums and cooperative apartments since there were so few of them and simply made a mistake in the law with regard to condominiums and cooperative apartments.

The end result is property tax in New York City depends on the properties class and it's history.

Cooperative apartments and Condominiums without the full 421A Exemption usually pays more, around $10,000 or more per year and usually more that a one to three family home, which usually pays less than $8000 per year.

The only way to see the differences in property tax is to look at a map that shows the assessed value divided by the market value.  The assessed value is the value that the property is taxed on.   The growth of the assessed value is also  limited by the S7000A law.

See https://nyc.tidalforce.org/ and search for any property and then look at the map that shows the assessment ratio and rates the closeness to the assessment limit.

See Tax Rating Map 

New York City Property tax is high for condominiums and cooperative apartments that do not have the full 421A exemption when compared to one to three family homes.

"The N.Y. State Law mandates that we value all Class 2 properties as income producing, based on their income and expenses. This means that when you see the Market Value that we assign to your property, it may not look like what you would expect its sales price to be. To get to your Market Value, we use a statistical model as a tool to find typical income and expenses for properties similar to yours (in terms of size, location, number of units and age). Next, we apply a formula to the income data to get to your Market Value. Class 2 properties include rental buildings, condominiums and cooperatives. All are valued as if they are income producing properties. There are variations in how we determine your Market Value depending on whether you live in a larger condo or co-op with 11 units or more, or a smaller building with 10 units or fewer. "

This means that condominiums and cooperative apartments market value DOES NOT mean the common definition of "market value"  "All are valued as if they are income producing properties." even if you live in your condo and you have no income, NYC Finance will compare against some similar property and come up with an income.  

"Residential property with more than 3 units including cooperatives and condominiums. NY State Law mandates that we value all class 2 properties as income producing, based on their income and expenses.  We use a statistical model as a tool to find typical income and expenses for similar properties to yours (in terms of size, location, number of units and age). Then we apply a formula to the income data to get to your Market Value. The law requires that we value co-ops and condos as if they were a rental buildings, even though they are not income producing."

You can see that the direct formula is not given.  The NYC Finance  uses "a statistic model" and "apply a formula"

At this time the best deal in New York City is two or three family homes.  They get the best treatment with respect to property tax and can be used to earn extra income.

Here's live maps that show how close properties are to the assessment limit by neigborhood

Live map of tax rating

Live map of tax rating