The energy of the gravitational waves will decrease with the square of the distance, but the amplitude will not. We can detect this in LIGO. This amplitude is also known as "strain". For more discussion check this page: http://spiff.rit.edu/classes/ast613/lectures/grav_i/grav_i.h...
The same is true of electromagnetic waves. The amplitude of EM waves decreases inversely with distance, and the energy decreases with the inverse square.
Your original comparison of EM waves to gravitational waves is only possible because you looked at the power of one, and the amplitude of the other. If you compare apples to apples, they're the same.
A question for typon: in light of this information, do you still believe that advanced enough civilizations would use gravitational waves for communication?
The equation for strain is: http://spiff.rit.edu/classes/ast613/lectures/grav_i/eqn_stra...