Commercially available TiO2 i.e. Degussa P25 has a mixed phase of Rutile (75%) and Anatase (25%). Its bandgap is ~~ 3.05 eV. This makes P25 nanoparticles only UV active and not Visible light active.
In your case, you are talking about TiO2 with bandgap more than P25 then it should be anatase phase TiO2 nanoparticles with bandgap of 3.20 eV.
Anatase phase of TiO2 is also UV active, but to make it visible light active either you need to dope it or make composite/heterojunctiion with smaller bandgap material. This should make it visible light active.
To answer in perspective of visible light activity of TiO2 then definitely once you decrease its bandgap, it makes the activity greater than P25 nanoparticles because more number of electron-hole pairs are generated in visible light.
and if you want to know with respect to UV light, then mixed phase i.e. P25 nanoparticles should have a better activity because of heterojunction formation between rutile and anatase phase.
I agree with the opinion of Dr. Saurav Sorcar in increasing the activity of TiO2 nanoparticals by modified the surface of it with doped some active metals such as Pt, Pd... or decomposed it with other semiconductor or sensitized it with dyes. Moreover the produced crystal size less then 10 nm will give special properties for Nanopowder compared with that have a crystal size from 10-100 nm. hence, the activity can be changed according to the used reaction.