A vacant flat is bought by someone who wants to move in. A rented flat is bought by someone who wants to run the numbers. Those are two different markets with two different prices – and the gap in Berlin is larger than almost anywhere else in Germany.
The reason is tenant protection: whoever buys a rented flat takes on the tenancy with all its terms (“sale does not break tenancy”). Notice for owner occupation is possible, but for converted flats in Berlin only after a ten-year lock-up, and rent can be adjusted only within the rent index and the cap. An investor therefore does not pay for the flat, but for the cash flow it produces.
In practice the price of a rented flat in Prenzlauer Berg is 20 to 35% below a comparable vacant one – the lower the rent and the older the contract, the larger the discount. With rent close to market and a recent, well-drafted tenancy it shrinks to 10 to 15%.