If I transfer $10,000 from the U.S. to India or ₹10,000 from India to the U.S., what net amount will I receive?

From US to India, when you will transfer US$ 10,000 as remittances, Regulation E of the CFPB (Consumer Protection Financial Bureau) will ensure, you will be given a breakdown of all the costs, and especially what you will receive (net) in India in your bank account.

The rates vary from provider to provider and what the exchange rate is for the day, but full transparency is provided for.

I cannot answer on the reverse.