After dire warnings on TripAdvisor about traffic on the Queens something Expressway, construction at LGA slowing things down, baggage claim at LGA "awful" and 4 hours being "really tight" it turned out that my arrival at LGA was 45 minutes early, baggage claim instantaneous, no line for a cab, no traffic, and actually was at the check in at JFK Terminal 8 before my flight was even scheduled to arrive at LGA.
LGW is always a speedier arrival process than LHR but I just don't like Gatwick much, at least from a departure point of view, arrival I couldn't care less but everything from layout, amenities, lounges, restaurants, etc are much better at Heathrow. All of my speediest attivals have been at Gatwick, straight through immigration, baggage already on carousel and taxi waiting (or car short distance away) so for an onward journey I would opt for Gatwick over Heathrow if the option was there but for me, my holiday begins with airport departure and I much prefer Heathrow for the start of my holidays.