A buddy and I had a race last year. He was LHR I was LCY. He got to the hotel in NYC about half hour before me and had to also leave his house half hr before me.
However, I hate queues and waiting in what can be a very long line at JFK immigration which is worth avoiding. I would rather be an extra 1hr on the plane than the arrivals rush.
At LCY you can pass security 20 min before your flight. If its delayed, they call. I dont tend to cut it that tight anyway, but theoretically thats at least 25 min saving on LHR.
I live equidistant from both. So I can leave half hour later to LCY. At JFK I have been through in 10 min, but also been stuck for 1.5hr behind some Iberia/China Eastern 747s or whatever. With Global Entry one would be quick, but I don't qualify.
The data used to be good and I valued that as well as the extra TP. These days I'm 50/50 which I take, though I do like the LCY service in general as its more personal. Crew are great and food is decent. A/V not as good, but survivable.