I am pretty sure it doesn't (much) matter which you use. After all, even on a heavily sailed boat we run REALLY low duty cycles on these gear boxes. Think about it, in a really busy day of sailing, that gearbox sees maybe 15 minutes of use. If you are underway 100 days a year, that's only 25 hours of operation, and that's a very generous estimate. I'd be surprised it in the real world we accumulated 100 hours in 10 years of full time cruising.
Far more important than grease vs oil is making sure you replace the shaft seals BEFORE they fail and let salt water in to the internals. I have those on a two year replacement interval. How did I chose that? Because after two years, there was not a trace of water inside the gearbox, and I see no good reason to push it further out than that. I also use double lip seals to help keep water and salt out.
The transmissions on my Lewmar electric winches are essentially the same as used on the furling system, and they get used a LOT more. Yet we rarely have problems with them. Why? Because they are below deck and stay dry.
One possible advantage to using oil is that if the seals fail the oil leaks out and make a mess you can see which (hopefully) prompts a quick repair.
On the hard at LMC,
Fort Lauderdale, FL