What should i use?
opengl or libgdx?
is it the same thing? which is better?

Use what you want and are comfortable with. In your other topic you said you know Android development and OpenGL so you should already be able to do games for Android. You can either work with OpenGL ES directly or though a framework like LibGDX. LibGDX automatically handles other things like asset loading/management, sound, etc. It also allows for deployment to desktop, the web, and iOS (with a license).

Thank you for the reply.
I really appreciate your reply. thanks 100 times. What i understand is that libgdx or game engine makes your life easier in coding. game engine uses shading language. while shaders like opengl, makes your code become longer or shall i say, hassle?
is this right?

If you use LibGDX or another engine, you'll still need to write your own shaders. OpenGL is a graphics library (Open Graphics Library). It lets you render using the power of the GPU. It is not, in itself, a shader. It can, however, use shaders to make pretty effects. Wiki has a nice reading on Shaders that you might want to check out. Depending on what you want to do, shaders aren't necessary.

LibGDX and other libraries or engines are there to extend OpenGL. In itself, OpenGL can tell the GPU to render things. It doesn't have window management, asset loading/management, sound (OpenAL does that), input handling, or anything else. It just draws. What LibGDX and other frameworks and engines do is give you access to (by handling) those things that OpenGL doesn't do alone.

Ok. I understand now. THanks for clarifying. So there are things that opengl cant do which libgdx can do. Nice. Thanks for the reply