There's always a default to the Gatwick Express and Victoria station, but Gatwick is accessible by a single train (overground, not tube although the overground trains often run in tunnels in central London) service from London Bridge, Blackfriars, City Thameslink, Farringdon, St. Pancras, Elephant & Castle, as well as Victoria, all train stations in central London, and with a transfer train-to-train from virtually any part of London.
Heathrow on the other hand has single train service only to Paddington which is almost central, then one train tube service on the Piccadilly line that runs diagonally across London, and then accessible to anywhere with a tube transfer.
Overground trains have more room for luggage.
Note that if you stayed within walking distance of St Pancras you would not need either a taxi or tube when entering or leaving London with luggage: arrive Eurostar at St Pancras, then leave to Gatwick on Thameslink train from St Pancras, or to Heathrow on Picaddilly line tube from adjacent Kings Cross tube station.
It can be confusing that there are tube and overground rail stations that share the same names, in close proximity, but are nearly always different entities. One exception I can think of is Farringdon where the tube and overground trains share the same tracks.