Ask yourself: Do I need tessellation, order independent transparency using sample masks, better texture compression formats, atomic counters in shaders, per sample fragment shaders, texture samplers (these OWN BTW and are also available in OpenGL 3.3), rendering using data from OpenCL directly without going through the CPU, advanced instancing or 64-bit floating point data support? 
Pure LWJGL should have better performance as you aren’t using a game engine and can tailor all the functions of the game yourself, but using a libgdx is easier and gets you results faster. I would recommend you to at least try out LWJGL, so you get some insight in how it works. That kind of knowledge is very useful even if you decide on libgdx later, as you’ll know how things work, which functions are fast and slow, e.t.c.
PCs will always have the best graphics. If you’re interested in making games with awesome graphics, you can’t really do that (as a programmer) with OpenGL ES. I’m not saying phone games look bad, just that you can only do so much lighting and shaders with that kind of performance. That 3D swordman game on the Iphone may look good, but it’s just some nice 3D models, textures and animations. The “programmed graphics” are just basic lighting and bump mapping. You’re not going to be able to implement ambient occlusion, tessellation, volumetric lighting, subsurface scattering, e.t.c. on a phone for a very long time. In my opinion, these damn phones are a huge step back for game graphics. It’s all left to artists to make games look good on those plaforms (not implying that programming itself isn’t an art xD). As I’m interested in graphics programming, I hope your future never comes, Cas, or that it comes fast enough so I actually have something to do in that future. 
