> when discoveries are made with the LHC are they made public

Yes. CERN is a publicly funded, shared facility; its users are universities. What it does has no direct commercial value.

> will another country investing in another one (or even a bigger one) discover anything that the European one hasn't?

Possibly. The proposed machine would allow more precise measurements of the Higgs boson's properties than the LHC. The best case scenario is that those measurements would turn up deviations from the Standard Model, which would point the way to something new.

To actually "discover" that hypothetical new thing, in the sense of directly detecting a new particle, would probably require yet another accelerator to be built (possibly in the same tunnel).

"What it does has no direct commercial value."

Well, apart from that "web" thing.... ;-)

I always think that was a great example of the complete unpredictability of research - fund one thing and get benefits you'd never have been able to predict.

Derivations of their work may be commercially valuable but to my knowledge CERN projects do not directly generate revenue.

The WWW was not a CERN research project, it was a hypertext system (far from the first one) developed by a couple of technicians working at CERN's office of documentation to facilitate the sharing of documents across its multi-OS, multi-protocol computing environment (at the time IBM VMS, DEC VAX, Apple Macs, PCs, and the NeXTstations used to develop the first WWW client).

It took off because it was free, open source and easily portable by design, but frankly, pretty much the same thing could have, and doubtless would have, emerged from many other large organizations with similar requirements (quite possibly an intelligence service like the CIA - let's not forget where Tor came from), even without a dime being spent on particle physics.

As for direct commercial value, CERN made it freely available to all, as it must. The closest it got to making some money off it was an Apple program to donate computers to the office of documentation.

And don't forget all the engineering work that goes into the magnets and data analysis tools. The internet falls into this broad category of components necessary for the pursuit of science that aren't the direct objects of research.

Science by it's nature isn't kept secret, results are shared and verified.

What a second LHC does is allow you to verify results independently. With one LHC you have to be extra careful about assumptions you made and what data might be being thrown off by local peculiarities.

Being at the forefront of particle/energy research is it's own reward. The results are only part of the prize. Learning how to build a LHC is probably just as valuable.

The LHC hosts multiple detector complexes. They are operated independently by different collaborations which compete with each other:

https://home.cern/science/experiments

They just happen to feed off the same particle beams.

The proposed Chinese collider would not be a second LHC; it would be a Higgs factory for precision studies rather than a discovery machine like the LHC.

Everything about CERN is in the public domain. By the way, while CERN is a European institution, research conducted at CERN isn't anymore that European: dozens of different nationalities work together in harmony with the common goal of sharing humanity's knowledge.