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Mechanical waves require matter to travel through so they can't travel, for example, through space. Electromagnetic waves interact with charged particles but not with neutral ones.

 

So your answer is, neither.

neither.

It is more like an electromagnetic wave than a mechanical one.

 

In electromagnetic theory you have an electromagnetic field that lives everywhere. You can solve the theory to produce waves in this field.

 

Now, in general relativity we have a gravitational field, known as the metric. The metric defines the local geometry on the space-time. The equations of gravity are much more complicated that electromagnetic theory. What one can do is linearise them and think about little fluctuations about a flat metric. In doing so we get the wave equation. These little ripples in the metric are the gravitational waves. They are small distortions in the local geometry, akin to the distortions in electromagnetic field.