Mind of Eye False basically allows the user to put up a better defense, and predict some of the enemies moves though to a lesser extent than Instinct because they don't 'see' or 'feel' the attack coming they just react to it better. If something is still quick enough to speed blitz them it will but they have the opportunity to make it not fatal.

[quote]Eye of the Mind (False) (心眼（偽）, Shingan (Gi)?, localized as "False Insight") is a natural talent to avoid danger on the basis of an innate 6th sense, intuition, or prescience, where accuracy of instinct has been augmented by experience - somewhat overcoming the problem of visual obstructions that appear in the course of combat. The difference between Eye of the Mind (True) and Eye of the Mind (False) lies in that the former is an ability that humans can obtain through accumulation of experience. The 'False' version is superficially similar, but in fact represents a natural instinct that cannot be obtained regardless of effort or experience—even though experience can refine its accuracy[/quote]

Extra Emiya's description of it is 

[quote]Capable of calm analysis of battle conditions even when in danger and deduce an appropriate course of action after considering all possibilities to escape from a predicament. So long there is even a 1% chance of a comeback, this ability greatly improves the chances of winning[/quote]

[@KawaiiKyouko]