Unlike most companies, Warren Buffet doesn't care if you buy his stock. The last close of BRK.A is at $99,000 and has an average volume of about 800 - meaning that if you hold that stock, you're almost certainly an institutional investor who's in it for the long run, and who know perfectly well what the company is like. For similar reasons, he doesn't need to project any images of modernity or customer-friendliness, if for no other reason than BRK has no real customers.
Most companies make fancy web pages to appeal to customers and inform them, to project a positive image for investors, or to provide a service. All Berkshire's web page is there for is to distribute some documents, most of which are updated annually or so. Hence no need for something fancy.
While you're there, have a read of the Owner's Manual and one of the annual reports, which are written as if you're friends with Warren Buffet and he's having a casual conversation with you about how business is going. He tells stories, he talks about individuals who have done well this year - but by the end you have a very good idea about how the company is doing, and you've probably learned something about finance (I don't have any shares in the company and I always read them). Also funny is the descriptions of the BRK annual meetings - known as _Woodstock for Capitalists_ - and the associated sales events from all the Berkshire companies.