Mechanism-based reasoning:
Both Bacillus thuringiensis and Bacillus sphaericus produce insecticidal toxin proteins, but their target specificity differs by receptor binding in the host gut. It is Bacillus sphaericus that is especially effective and persistent against mosquito larvae because its binary toxin binds strongly to receptors in the mosquito midgut and can recycle in cadavers, giving longer residual control in organically polluted water. Bacillus thuringiensis (in its general form) mainly targets other insect groups such as lepidopteran larvae rather than mosquitoes, so claiming it is broadly effective against mosquitoes overstates the case.
So, Statement I is incorrect and Statement II is correct.