To redesign the logo of a company, the leaders have to decide have to decide whether they want to do an evolutionary step in which the logo is being developed or to do a revolutionary change in which the old logo is replaced by a new one.
Often logos are slightly modified and lifted to the third dimension as seen in the example of Arby´s. Or you can reduce elements which is seen at Best Buy, Wendy’s or Domino `s. Very exciting is the revolution, when the old logo is replaced such as in City of Melbourne, Seattle’s Best and Wacom. Very inspiring for your own logo designs or the logo designs of your customers.
By the way: You see the old logo on the left or above the new logo. It depends on the format.