What do you think about this?, which is more efficient? advantages disadvantages. I must choose one of them

Use both.

You have to remember that you''re unique, just like everybody else.

Id say Geomipmapping + QuadTrees = Winnner!

Quadtree and geomipmapping together? how?

You might want to read a bit more about both of them since I think you don''t undersand both of them fully. They mainly solve different things. QT is used for culling while GMM is for LOD, so there is not problem mixing them.

You should never let your fears become the boundaries of your dreams.

What? I have read some papers, I think that the QT hierarchy is very good for culling but the QT was created for LOD. For example this paper.
Real-Time Generation of Continuous Levels of Detail for Height Fields Stefan Roettger, Wolfgang Heidrich, Philipp Slusallek, and Hans-Peter Seidel. http://www.vis.uni-stuttgart.de/~roettger/data/Papers/TERRAIN.PDF

The quadtree is used to cull out large batches of terrain which aren''t visible in the frustrum, and geomipmapping is used for LOD. They are quite different from each other, but they work well as a team.