First off, I see a lot of reviews stating that they're not exactly sure what emos is or sounds like. Defining emo is difficult, as it is a broad category, but it can be divided three ways:
Power pop (similar to geek rock) - Promise Ring, Weezer, etc.
Emo - Sense Field
Post-hardcore - Thursday, Texas is the Reason
While Thrice tends to capture a fair portion of the post-hardcore sound, I would say they're closer to punk and indie rock. "The Illusion of Safety" represents this amalgam with speed, aggression, and melody, perhaps more than the other two major releases, "The Artist in the Ambulance" and "Idenity Crisis".
Thrice separates themselves from other bands of these genres with their intricate strumming and patterns, ranging from the metal breakdown near the end of "To Awake and Avenge the Dead" to the bluesy intro of "So Strange I Remember You". The songs on this album are cleaner and catchier than those on the more hardcore-laden "Identity Crisis", while being less mainstream and metal-sounding than "The Artist in the Ambulance". Overall, my favorite release by Thrice, as it starts strong, ends strong, and kicks rear everywhere in between.