Our claim on South China Sea is far stronger because we told the whole world in 1945 about the 9 section line and nobody objected until the 1970s. Again, we claim all the islands within the 9 sectioned line, we don't actually claim the whole area as territorial sea. This is a point that Western propaganda has deliberately been trying to conceal.
Vietnam's drilling within the 9 sectioned line isn't necessarily within our EEZ, and it is relatively close to their shoreline, but because the countries around the South China Sea have not settled on EEZs, the whole area is disputed. So india should not step into the dispute on Vietnam's side until China and Vietnam have settled our EEZ. Remember, China and Vietnam settled our EEZs in the Bay of Tonkin already, and both sides are peaceful.