The upcharge for a PTHP (Heat Pump) from an PTAC (Air Conditioning only) isn't huge money, and well worth it. Look for units that have variable speed scroll compressors & blowers and they will hit mini-split type comfort and quiet sound levels, if not quite identical in efficiency.
Whether the radiators are actually cheaper to operate than a PTHP in heating mode depends on the fuel, boiler efficiency, and distribution losses. In many places (even higher-priced electricity markets) a mini-split is cheaper to heat with than with an oversized 80% AFUE boiler on a system with significant distribution losses (say, the boiler is in the basement, serving a second floor apartment, with uninsulated or barely insulated heating pipes.) During the shoulder seasons when the temps are in the mid-40s or higher the efficiency of variable speed heat pumps SOAR, and will almost always be the cheaper to run than covering those loads with a fossil-burner.
All good heating system designs start with a careful heat load calculation (ACCA Manual-J method, or similar). Apartments typically have very small heat loads compared to the output of ANY steam or pumped hot water boiler, and it just might be cheaper to heat with PTHPs, but we really can't say until the calculations are run. The heat loads of an apartments other than the top & bottom floors are a function of the exterior wall construction and window types, and the square footage of both the wall & windows, not at all about the size of the apartment, only the exterior surfaces, their U-factors, and the anticipated temperature difference. NYC's 99% outside design temp is +15F, so if you assumed a 70F interior temp that's a 55F temperature difference. You could design for a colder temp/bigger difference, but that won't make you any more comfortable, and leads to lower efficiency if oversized by more than ~1.3-1.5 or so. (Most cast iron hydronic boilers would be 5x oversized for a typicial apartment's heat load, and running well below the nameplate AFUE efficiency.)
Cooling loads are a bit more complicated, with solar gains as well as parasitic gains from internal sources. If it's a top floor apartment the amount of ceiling area and the insulation in the attic space or roof matter too.
Measure it up describe the wall & window construction a bit, and we can probably ballpark it pretty reasonably. I'm guessing that any PTHP with sufficient cooling capacity will be oversized for the heat load, which would make a modulating version even more desirable.