Besides load times or transitions between levels or between fast travels and the speed at which you actually enter the game for the first time, the major benefit of having a game fully designed around an SSD will be in how much and how quickly they will be able to stream different information in for the game to take advantage of in meaningful ways. Trees, geometry, highest quality textures, parts of the world out into the distance, visible enemies.
Hell, it can change the range of enemy detection and how they engage the player possibility in that they may be capable of more complex behavior from much further out distances because the console as well as the SSD can "activate" them faster if that makes any sort of sense. Either way, the worlds should be able to look a lot more rich and dense as a result of an SSD. How you can maneuver through it can likely also be drastically enhanced, as demonstrated by Sony's spiderman demo.