Well, many of these tunnels, including the one the LHC uses, have been refurbished multiple times already. Cern's main ring was built to be somewhat future-proof, but that was a long time ago. A google search came up with The history of CERN, which dates the groundbreaking to 1954.
In accelerators you have two basic designs: linear and circular(ish). In linear accelerators each boosting element (RF cavity or whatnot) gets one chance to give the beam particles a kick, so the energy is limited to how hard you kick (limited by technology) and how many elements / how long (limited by budget).
In circular accelerators you are limited by synchrotron radiation. At some point the energy pumped into the beam matches the energy lost via synchrotron radiation. To move in a circle you have to accelerate inwardly, and an accelerating charged particle radiates light. At particle accelerator energies, this radiation is in the x-ray spectrum. You can reduce the loss by using a larger ring -- a smaller curvature requires less centripetal acceleration and hence less radiation loss. You can also of course build stronger boosting elements, but the radiation also heats the beamline and surrounding superconducting magnets, so it's not "that simple."
The other thing to vary is the kind of particle accelerated. Electrons have a very small mass and lose a larger fraction of their momentum to synchrotron radiation. SLAC and KEK are linear accelerators that use electrons. (Cornell's CESR is a ring that accelerates electrons too, but at lower energies compared to these others.) Protons are the other obvious choice, which is what Fermilab and CERN's LHC (after the upgrade) are accelerating. Being much more massive, the protons slough off less of their momentum to synchrotron radiation and can be accelerated to higher energies given the same size ring. The disadvantage of protons is that the energy of the proton is shared among its three quarks (and gluons I think) whereas the electron is truly singular as far as can be told.
I've been out of touch lately but as of at least 8 years ago three proposals were being discussed: VLHC -- big ring accelerating protons. Next Linear Collider (NLC) -- long linear accelerator for electrons. Muon collider -- a smaller ring (actually with straight sections like a track&field track) that produces and accelerates muons. Muons are just like electrons only 200 times more massive and is unstable with a half-life of 2 microseconds. The muon collider was thought to be an ideal Higgs factory, but with a lot of design challenges. One of the main challenges is to not only accelerate the muons before they decay, but also collimate, or "cool", the beam very fast as well so that you can create as many head-on collisions as possible.
So the news that the VLHC design is currently in favor is interesting, but this is hardly the first time the issue has been discussed and I doubt it will be the last. Several years ago the NLC design seemed most favorable, but this would, by its length, be limited to a specific design energy and probably be built to produce Higgs, Higgs, and more Higgs. It seems to me like a VLHC would have more discovery potential for more massive Higgs particles, signs of supersymmetry, or whatever else might exist.