In my opinion, the biggest factor in the success of a PbP game is the ability of all participants to tell a story, particularly the DM. In a tabletop game, even a mediocre DM can run a fun game as long as everyone is intentional about helping the game along. But with PbP, the players cannot as easily compensate for a poor DM.

As a side note, I feel that 4E combat is fundamentally ill-suited for PbP because you have to use a battle grid and that makes for very slow and tedious combats in the PbP medium. Too many powers are directly tied to tactical movement around the battle grid. Conversely, I’ve played many PbP games with the 3.5 ruleset (and no grids) and it works wonderfully.

The best thing about PbP is that roleplaying truly takes center stage and combats can become highly cinematic.