Great work @sagarpreet!
This might get rambly because there is no right answer but I'll try to explain why and what then.
The first thing you need to understand is that all AQ indices are designed for COMMUNICATION purposes so the question is not "should I report concentrations or indices?" but rather "what am I trying to communicate?"
There are many indices and all of them serve different purposes.
Some are "regulation" related so they refer to the corresponding regulation limits. These are pollutant dependent so you can have a high index for PM2.5 and a low index for Ozone at the same time which will mean that concentrations of PM2.5 are near or above the standard (whatever that is) while Ozone concentrations are well below the standard.
Now, there is an argument that the standards have very little meaning for the general public as their meaning is unclear and they are defined on many different time bases. So, that's where the "health effect based" indices come in. They try to communicate "risk to people" rather than "state of the air" so a high index value would mean that there is a high risk of a health impact (whatever that may be) with these conditions... that's what the AQI tries to do
In general, if you want people to do somehting, show them something they can understand so AQI's are much more useful for that BUT you need to be VERY careful with the averaging times you're using and you need to be very transparent on where you got the calculations from because if you tell people that their air is OK but it isn't, you're in trouble.
So ... decide what you want to communicate and run with it documenting your sources.