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Your question is a little ambiguous, but Euler Circles, sometimes called Euler diagrams, are generally regarded as far superior to Venn diagrams from a cognitive perspective since they exploit topologocal properties that match semantic properties. This exploitation means that they are well-matched to what they represent. In general, Euler diagrams do not restrict to the use of circles and are formed of arbitrary simple closed curves, like Venn diagrams. It terms of expressiveness, if one allows only the use of simple closed curves, then Euler diagrams are less expressive than Venn diagrams. However, frequently Euler diagrams are permitted to use shading (which Venn used in his diagrams to assert the emptiness of a set). Under these conditions (i.e. simple closed curves plus shading) Euler diagrams are equivalent in expressive power to Venn diagrams. Moreover, if you don't like the idea of using shading, you can remove the constraint that the closed curves must be simple and, again, this results in Euler diagrams being as expressive as Venn diagrams. I hope that helps.

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Q: Why Euler circle method is worse than Venn diagrams?
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