As stated on [classofheroespsp.wikispaces.com/FAQ]
Q - What is an EX Map?
A - While traveling through labyrinths, when you pick up a item off the floor (shown as a diamond on the interface), there is a chance that your map will "break". However, if you have an EX Map, it will not break.

Personally I never had a map brake on me and even if it did I could just cast a level 1 black magic spell called Sight which creates a map I can use for the duration of the dungeon.

regular map breaks
ex map doesnT

An EX Map counts as another item towards your item completion percentage on a save file.

The EX Map is unbreakable. The regular Omega Map is unbreakable, and making an Omega EX Map does essentially nothing but 'fill out' an item slot in the library. It takes 10 normal maps to alchemize into an EX Map.

To have a map break, pick up a random blue floating crystal in a dungeon and get a 'gust of wind.' The wind tears all normal maps (not normal Omega Map). The wind does not do anything to the 'SIght' spell which acts like a map.