Earlier quoted context omitted.
I don't have the statistics at hand, but I'd say it's likely more. The remarkable safety of airliners doesn't extend to smaller aircraft.
It actually does, the problem is that the same restrictions do not apply. A very large amount of private aircraft related accidents happen because of extreme conditions in which a commercial airliner would have not been flying under in any case. Privately owned aircraft also tend to be much less well maintained and their pilots have considerably fewer flight hours than big or small commercial aircraft. This is when "…
For this specific service, there are a couple of things that do make it inherently less safe than being in a brand new 747-800. Specifically, there's much less redundancy and fewer emergency options for when something goes wrong. If you lose an engine on a 747 then you just keep going. If you lose an engine, or rather the engine, on a Manhattan-JFK helicopter flight then you're going down extremely fast and you have few or no good options for where to put the thing. It's similar for suddenly encountering a flock of geese (the odds of a safe landing in the river with a 100% survival rate are considerably lower with a helicopter than with an A320), fuel exhaustion, or a sudden pilot heart attack (I'm guessing there aren't two pilots in these things).
Mid-air collisions are another potential danger. I'm guessing that a helicopter like this doesn't have a TCAS system, and not all of the airspace in question requires ATC clearance. Nine people died in a helicopter/airplane collision in NYC in 2009, and it could happen again.
I don't mean to paint an excessively bleak picture here. I'd have no qualms about taking a flight on one of these helicopters, aside from the price. But at the same time we shouldn't kid ourselves by thinking that it's safer than taking a car, let alone as safe as an airliner.