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The Lawnmower Man - a simple man who is turned into a genius through the application of computer science and possesse a telekinesis and telepathic power on high level.

http://www.youtube.com/watch?v=YCxFGxqLsHE

Vs

Professor Charles Xavier from X-Men - a most powerfull telepath on the world.

http://www.youtube.com/watch?v=T6tcNn8VMKw

The professor X was asked for help in stopping Jobe which as a result of conducted experiment on it went crazy and slipped from under of control.
The battle is taking place in the laboratory where Jobe was turned into the lawnmower man it is a mental battle.

Whether the professor is able to stop the lawnmower man?

If it's soley a mental battle then Xavier should win due to experience.
Experience goes a long way in Psychic battles. There a alot of tricks. Like Inception.

Though the Lawnmower Man would be a hard shell to crack do to the extreme amount of knowledge and comprehension LM has now achieved.

Xavier would have to hit him fast and melt him out. He's probably one of the few characters who can stop LM under these stips.