Personally, I think OpenGL 3 is an era change version, akin to Direct3D 8. That was the time when API shifted from Fixed Function Pipeline to Programmable Pipeline. Everything else after that period is more like a incremental changes. So yes, the OpenGL portion itself is modern enough.

The another paradigm shift is in the DirectX 12 era, where the API gets more into the bare-metal level. OpenGL does not move into this direction, instead Vulkan is created with lower-level design. 

Personally I think if you don't need to squeeze out every bit of performance, staying in OpenGL might be a good idea. The idea of programmable pipeline is still applies in DX12 and Vulkan, so the main concept is still the same although there would be more work to do. 

I think any OpenGL with shaders (GL 2 ES 2) is still plenty modern.. and it's forward compatible.. where as the newer versions aren't backwards compatible.
That might not mean much, but it's a smaller subset and less complicated for beginners.. but on the other hand you miss out on new features.

Another data point to consider is that OpenGL 3 is not API-compatible with OpenGL ES.  OpenGL ES is considerably more widespread: it's used on mobile and embedded devices rather than Linux PCs and a few Microsoft Windows PCs.  OpenGL ES 3 is pretty much a proper subset of OpenGL 4, so your best bet for a "modern" OpenGL is to learn OpenGL ES 3 -- but that said, starting with OpenGL 3 tutorials will not hurt because it sets up the programmable-pipeline concept.  It's mostly that the API to set up the data transfer between CPU and GPU, and how the shader receives and processes those data, became much more generic with the newer versions.

4 hours ago, Bregma said:

Another data point to consider is that OpenGL 3 is not API-compatible with OpenGL ES.  OpenGL ES is considerably more widespread: it's used on mobile and embedded devices rather than Linux PCs and a few Microsoft Windows PCs.  OpenGL ES 3 is pretty much a proper subset of OpenGL 4, so your best bet for a "modern" OpenGL is to learn OpenGL ES 3 -- but that said, starting with OpenGL 3 tutorials will not hurt because it sets up the programmable-pipeline concept.  It's mostly that the API to set up the data transfer between CPU and GPU, and how the shader receives and processes those data, became much more generic with the newer versions.

If I'm not mistaken, one of the OpenGL 4 and GLES 3 releases are to consolidate the 2 api. GLES3 became a proper subset of GL4 since then. I can't recall what release it was, probably 4.0 and 3.2 ....

Anyway when I was learning GLES (which I quit eventually, had no use of it back then), I find coding GLES on the PC a bit painful, especially the project setup (If I'm not mistaken, I had to install AMD's SDK). I had more success in OpenGL, as it's shipped with the VC++. Writing GLES to run on the mobile was proabably easier, but I also find debugging on the mobile phone a bit annoying as well (it reminds me of my NintendoDS day....).

The situation might have changed since then though. You might be able to create a GLES context with breeze. I don't know. Been away from coding the graphics api directly for quite a while now.