Bharat will probably still have clashes with Pakistan and China. Dravidian may be more neutral and both would be members of the Non Aligned League. Both would have centrally planned economies post war. How long they last before liberalization may vary.
I just thought of something. I read on the wiki recently that during the partition Bengal was forbidden/not-given-the-option to go for independence. What do you guys think would happen if that was attempted? Would there still be a partition between the areas? I can see the vote maybe being split between Pakistan and Bengal, Perhaps with a threeway tie if West Bengal is still in the voting unit. So long as the borders are clear enough, and both Bharat and Bengal treat Hindus and Muslims in the borders reasonably well (maybe through use of many before vote agreements between parties, and making it clear that no one has to move no matter the results) then perhaps relations will be amiable. Though considering how badly things went in Kashmir, and how Over the years India invaded basically ever single disputed area, using reasons that contradicted each other (listening to the Hindu population instead of the Muslim ruler in one place, versus the Hindu ruler and Muslim, Sikh, and Buddhist majority in another).
By the way, how you guys think relations between Dravidia and all the other countries would be? So long as Christians (who had been in the area for over eighteen hundred years) and Muslims got to continue to live life as always I can see the Europeans being happy with them, and for good relations with the Phillipines in the future, perhaps also with Malaysia and Indonesia. I know a lot of Muslims came from over there to Indonesia, but I wonder which area the Hindus of Bali came from. Depending on the borders (as we are probably having Bharat trying to take the north of the Presidencies of Bombay and Madras) France and Portugal will border both Dravidia and Bharat so long as the Portuguese treat the people of Gao fine, perhaps also helping industrialize, they might be left alone. France might give up their specks without too much trouble after Indochina is lost, though with compensation paid for French property, as well as treaties for economic openess. De Gaulle and others might like the idea of Madras coming to be closer to Paris than London once more, though is likely to be a pipe dream. The Maldives are far off enough to not worry about, but the Lakdashweep islands are nearby and might be desired by Pakistan, who tried seizing them IOTL but got beat to the punch. Sri Lanka... well, hopefully things go well between the Sinhalese and Tamil. Mysore will be surrounded by the Dravidians and should probably play ball, while the ruler of Hyderabad might try to spin things off to keep himself in charge, since he would have two countries bordering him rather than one. Would be a tad difficult for him though. And lead to some tension on which Indian state gets the land.