With today's easy access to information, do museums have a place? I can think of four reasons why museums are still relevant:
They show original items. Some things are really one of a kind, or in very limited supply.
They organize things professionally. Wikipedia and the like are great repositories of facts, but can easily become piles of facts instead of a coherent whole.
They can immerse you since they don't have to fit the exhibition into a computer display. Especially when the items on exhibition are one of a kind, seeing their true size, shape and color brings you much closer to the theme than a jpeg on your monitor can.
They can pay to have exhibition material created. For example, the German museum had a very good CG animated film about the Berlin airlift. Making such a film costs money and may not be possible for a free website.
The Jewish Museum has some originals, but the greatest strength of the museum is in how it immerses you. The building itself is a masterpiece, being a cross between a Star of David and a line of barbed wire, zig-zagging along the grounds and cut through by laser-straight voids that cut through all floors. Just walking through the building is an experience that you can't get anywhere else; the museum itself contains nothing that you can't find on Wikipedia, but the experience makes it well worth a visit.
The exhibitions are well organized. They presented some facts that I didn't know, but their value laid most in the organization - the facts themselves tended to be either basic knowledge or trivia. They do a good job framing those facts, though, and I would recommend visitors to Berlin to visit the museum. It fills in some blanks that you may have, and does a good job of really immersing you in the joint history of Germany and the Jews.