Less likely to miss functionalities from the old code base.

Indeed. In any large code base that's grown up over a period long enough for the original developers to have moved on, there are going to be chunks of essential functionality that aren't well understood. When you rewrite (and miss the misunderstood functionality), you're forced into reactive rediscovery under fire when something that people depend on suddenly no longer works. Not a fun place to be.

Joel Spolsky had a post a while back called Things You Should Never Do, wherein he claims that rewriting working software is a huge mistake. He lays out some good arguments.

If you choose to go the refactoring route, Michael Feathers book Working Effectively with Legacy Code might provide you with some good tools. He tackles the problem of how you retrofit tests onto legacy code in preparation for adding new features (which often involves first making the code safe to refactor).