Holy See (Vatican City) is about 136 times smaller than British Indian Ocean Territory.

British Indian Ocean Territory is approximately 60 sq km, while Holy See (Vatican City) is approximately 0 sq km, making Holy See (Vatican City) 0.73% the size of British Indian Ocean Territory.
Tip: This to-scale comparison of British Indian Ocean Territory vs. Holy See (Vatican City) uses the Mercator projection, which distorts the size of regions near the poles.

Compare further: Holy See (Vatican City) vs. British Indian Ocean Territory