I'd hope that a train from Cologne to Berlin wouldn't cost more than the 250 euro compensation for a cancelled flight (assuming there weren't circumstances that negated this compensation).
I'm still trying to make sense of when Ryanair might be on the hook for hotel expenses. The EU261 letter from Ryanair only mentioned hotels in the context of a flight rebooking (e.g., now flying out the following day) but certain news articles have talked about getting reimbursed for additional/unexpected expenses that resulted from a cancellation (I opted for a refund + 250 euro since the Friday flight was cancelled and the next scheduled flight on Monday would only get me there in time for my return flight).