My take on the Indian Navy 3rd aircraft carrier:-
The Indian Navy wants a 3rd aircraft carrier so that at any given point of time atleast 2 aircraft carriers are at sea protecting India's interests.
As per the IN, it needs a 65,000 tonne carrier with electric propulsion.

Since 2015, the USN has worked with the Indian Navy in designing the INS Vishal.
The problem here is that while US is undoubtedly the king, it has no experience in designing smaller aircraft carriers and all USN carriers are nuclear powered.

Initially, the idea of nuclear propulsion is great, but as per some estimates the nuclear reactor would cost $2 billion alone, so this proposal was dropped and conventional propulsion proposal is being pursued.
EMALS is power hungry, so I hage my doubts whether..

conventional propulsion would be able to power an EMALS system.
So the other option of INS Vishal being based off of the Royal Navy QE class aircraft carriers seems quite lucrative to me.

It ticks 2 very important boxes:-
1) 65,000 tonne displacement
2) Integrated Electric Propulsion
It has the capacity to carry 60-70 aircraft(both fixed and rotary wing).
The QE class was initially envisioned to be CATOBAR carriers but was later dropped in favour of STOVL..

due to mounting costs.
Britian has proposed to build India the CATOBAR variant of it's QE class AC,
Britian built the STOVL QE class at price of £3.1 billion per ship.
The CATOBAR variant of QE class would not cost more than £5-6 billion, almost as much as half of US proposal

Britian still has the original designs of the CATOBAR variant of the QE class which means that it will not have to go around modifying the STOVL QE to fit the catapult system and the design changes to the deck.

Most importantly, it would rejuvenate India-UK relations which needs a complete reset in light of Brexit.

The proposed CATOBAR variant of Queen Elizabeth class aircraft carrier