@Paul-and-Sherry0, hello! I looked for your listing and compared it to the other listing you included as a sample.
I saw some differences from what you describe.
1. The prices I saw are not very different. Yours: $78, his $98. Certainly his is not double yours currently.
2. I don't see his listing as being booked more than yours. In fact, your calendar seems completely unavailable every single day in January, February, and all of March up to the 24th. His calendar is almost completely open in January.
3. As to comparing the listings: they both seem like very fine places to stay. If I were pressed to name a difference, in the photos your townhouse looks like a very clean and lovely home; the furniture and appliances are from a few decades ago.
The other listing gives the impression of being more modern, with decor, furniture, and appliances that are very current. (He mentions a recent renovation and all new furniture / appliances).
4. Your reviews / ratings are markedly better; his ratings are less than 5-star in 4 of the 6 sub categories, and less that 5-star overall. Your ratings are 5-star for everything but Location.
This is a very slow time of year for most travel. Even for San Francisco (which does not suffer from extreme winter weather) listings have to discount heavily to try to fill your Calendar in December.
I'm not sure you are doing anything wrong at all, and I'm not sure this other listing is doing much better than yours.
The biggest thing I would recommend is to try to provide a more modern and up-to-date look. Visual appeal can count for a lot in this business.
As to doing research, have you tried looking at AirDNA, or the free demos at Wheelhouse and Beyond Pricing?
These resources will give you more information in less time than scrolling around the AirBnB map.
All 3 resources let you do a basic analysis of your specific property, and Wheelhouse and Beyond Pricing let you enter your actual AirBnB listing to see their suggested pricing for free.