What are the advantages of each?
I don't know about you, but for us (my wife and I in Northamptonshire) Gatwick is more convenient by train for us. We take a train to St Pancras and go downstairs and take another train right to the station under the airport.
Heathrow is more convenient for us if we are driving, it is about 45 minutes closer.
From you, I don't know.
If you're flying out of Denver, you have the choice of British Airways nonstop to Heathrow and Norwegian Air Shuttle's inexpensive nonstop seasonally into Gatwick.
The question is how far in the future are you looking to go? Norwegian has a temporary reprieve on its money problems with bondholders at the present time. But are they going to be around in the future?
I always prefer non-stops to connecting flights. And looking through March, 2020, the airfares for British Airways is not bad in the mid $600's. I'd go with them.
The advantage to Heathrow is that it's on the tube, so for relatively little money you can get anywhere the tube goes in central London in about an hour or less.
The advantage to Gatwick is that it's a somewhat smaller airport, and you can take the train to Victoria Station. You do not need the 'Gatwick Express' - it costs more and only saves about 5-10 minutes max. The 'regular' trains that stop in Gatwick and Victoria only make one or two stops between them, take about 30 minutes and cost less. If you are staying anywhere close to Victoria that makes the most sense. Of course you can always change to the tube once there to go somewhere else in central London. The train costs more than the tube from Heathrow but some people think it's more comfortable.
Gatwick is a bit smaller than Heathrow, which on arrival I don't think makes any difference, but for the return trip it is marginally easier to navigate.
We always go to Heathrow because we can get a non-stop flight from Baltimore. We take the tube into the city.
Assuming that either arrival airport is located satisfactory in regards to your final destination, my suggestion is that you investigate available flights from your departure airport to both destinations.
Available flight times and direct flights vs connections are different. For are flight costs.
The advantages/disadvantages of each will be more apparent if you evaluate the costs/flight availability of each.