Are you sure its a Series 3 HD XL? The label on the back would say TCD658000. Under Settings, System Information screen, it would also say the model in the first 3 numbers of the TSN (Tivo Service Number), the Tivo software's first 3 numbers also.
If it is, then it does not support 1080p. The only resolutions are 480i, 480p, 720p, 1080i.
If you are able to set 1080p then its a Premiere (Series 4) or Roamio (Series 5). Premiere has SD and HD menus which are selectable, but Roamio only has HD menus.
Original S1 (Recycle Heaven)
Series 2 (PLS, sold)
TiVo HD (XL, PLS, "652")
Juliet Basic (4XL, PLS)
The TiVo Apocalypse begins on Sat 2013 Feb 16 00:00 GMT!