I see polymorphism vs if/... more as a tradeoff. For example:

Suppose the program has to make a choice. When the choice exists only in 1 place, use an if/switch. When the choice exists in multiple places, polymorphism centralizes it and quickly becomes the simple option.

For example, a change in law required us to make a choice based on a date:

   If (thing.someBusinessDate < 2010-06-01) { doTheOldWay();} else{doTheNewWay();}

after a while, a few edge cases sprang up, and we got variants of this code hiding in multiple corners. Then the law changed again with a new cutoff date. So we adapted to polymorphism:

  interface TheWay{ edgecase1(); edgecase2();...}    
  class TheOldWay implements TheWay{...}
  class TheNewWay implements TheWay{...}
  class TheNewNewWay implements TheWay{...}
  TheWay wayDetector(thing){/* all the ifs here */}

Unfortunately, adding just one more 'if' was always the cheapest choice. The refactoring was nevertheless clearly a better choice: it enabled us to point out more forgotten edge cases, avoiding costly mistakes.