Johnson would have been motivated and prepared for Dempsey. But that would not have been enough. Even during his prime, which was actually before he won the title, Johnson would have his hands full against an aggressive prime Dempsey. Styles make fights and, while Johnson could certainly outbox Dempsey, he would always have trouble with Dempsey's aggressive style.
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A fight at this time would have been much like Tyson v Holmes. The wiser Johnson would use his skill to ward Dempsey off early. But Johnson would never be able to keep it up. Dempsey would break through at some point in time and put an end to the matter.
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Dempsey by KO in 4.
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If both met during their respective primes, in 3 separate scenarios, I see Johnson taking the series 2/3, winning two on points and Dempsey one by KO.