Considering a scenario that one is hiking a lot in the indian sub-continent, what is better in order to mitigate the issues one may face due to bright sunny day? A hat or a simple cap?
I assume by hat you mean mean a full-brim hat, while by cap you are referring to a baseball cap (brim in front only)?
Regardeless, in all instances of hiking anywhere with intense sun, your best bet will be: a hat
The wider the brim the better, to keep the sun off your neck, ears, nose and shoulders.
For sunny, arid regions: consider a thin airy straw-type hat that allows good circulation around your head while providing sun protection.
The straw will often hold water fairly well, and that along with a sweat band tied around it is great for evaporative cooling: Soak and repeat for a personal air conditioner.
Tighter weave, treated, or gore-tex full brim hats are great for rainy regions, keeping the water out of your eyes and off your neck.
A hat. Or a cap with a sun shield.
It covers the back part of your neck and ears from harmful sun rays. Also, make sure that the cap is UV protective. A simple hat might not do the trick of blocking out the UV (It might protect you from direct sun though).
One disadvantage of a hat is that it blocks your peripheral view (i.e if the hat droops on the sides). But for me, the advantage of protecting your neck and ears from severe sun burns outweighs the vision aspect.
Another issue to think about is whether you will have a backpack or not (and how high it rides up). Anyone who's tried backpacking with a sombrero knows what I mean - the hat is constantly whacking the pack and it drives you nuts.
Also consider (as mentioned above) the wind - a string through the hat that can be tightened around the chin works, as does a "leash" tied from the hat and clipped to your collar. A lost hat means sunburn even more than the wrong hat...
Another option is a cap/visor with a bandanna. I like doing this when I expect windy conditions. Wide brimmed hats (superior in most other circumstances) will have more wind resistance and can become quite the nuisance. When you can wear neither a hat nor a cap (because you are wearing a helmet, for example,) the bandanna alone is quite effective!