I don't think much will change. BH has a succession plan in place (Buffet has written about it on the company's web site), and the successors seem to have the same philosopy as he does.
In the short term (5 years or less), not much.
In the long term (in the next 20 years), depends on whether the "Buffett Method" is adhered to and whether it will continue to "work" in the future.
Nothing dramatic will happen.
Do you think Berkshire will continue to be a leader in the stock market, in terms of the price of each share?