I think it's fair to say that Rahul and Babar are completely different batsmen.
Babar cannot chase any high scores on any ground and that will REMAIN A FACT UNTIL HE DOES. Infact, the proof is on the opposite side, when he chugged away at a useless century while chasing 360 against Australia in an ODI because that was his ceiling. Babar is more a of a complete player, as he will almost guaranteed hit you a 50 every match, but most of the times it won't define the match. However, it will ALWAYS BE useful innings in the context of the game.
Rahul is more of a hit and miss player. If he fires, he WILL DEFINE THE MOMENTUM of the match and will decide the fate of the match more often than not. Rahul has a higher ceiling chasing or setting scores because he is more aggressive naturally. Rahul however WILL FLOP MORE TIMES than Babar because of his stroke making ability.
In a team like India, which has a rich heritage of batsmen, Rahul is almost a luxury. If he fires, he will win you the match. If he doesn't, you have Rohit or Kohli to change the complexion of the game. Pant can hack around a few as well and then upcoming Prithvi Shaw is a huge talent.
However, in team like Pakistan, Babar is almost a necessity. If you don't have Babar, we are collapsing to 150 all out almost every match.
I can see why Pakistanis tend to over-rate Babar, who might be a great player someday, but at the moment is a better consolidator than a match defining winner, and I can see why Indians don't rate him that highly.
And that is precisely the reason Indian tend to over-rate Rahul because they have way too many consolidators in the past.
In my opinion, I would take Rahul but only because I like aggressive stroke makers more than pretty consolidators in any situation in any match.
Kohli and Rohit are in another league and anyone who thinks Babar is close to them should get his head checked.