Simply build up a URL like this:
https://alantgeo.github.io/mapbox-compare-maps/#left=USERNAME.TILESET&right=USERNAME.TILESET&mouse=true&access_token=ACCESS_TOKEN&location=ZOOM/LAT/LON
left
required Style ID of left map (username/styleid or username.tileset)right
required Style ID of right map (username/styleid or username.tileset)access_token
required Mapbox Access Tokenmouse
optional If true the swipe follows the cursor. (Default: false)location
optional ZOOM/LAT/LON default location. (Default: Style default location)title
optional If true the style titel is shown. (Default: false)