Hayabusa:
What I was wondering is what specific benefits (if any) do we know we would have gotten from the SSC's much greater collision energies? I believe that Tevatron would probably have eventually found the Higgs particle if it had been able to continue operating, does that mean that the SSC would've simply produced data faster than the LHC or are there any predicted discoveries that the LHC simply isn't powerful enough for?
		
		
	 
.
There is something called the hierarchy problem. Greatly oversimplifying, it's the problem of explaining why the Weak force is 10^32 times stronger than gravity and the strong CP parity problem which I won't go into but which wreck the Standard Model, which you may recall is a patchwork system intended to explain the relationship between three of the four fundamental forces of nature (gravity being  the exception since its beyond current  theories)
An extension called supersymmetry fixes these problems by proposing that bosons have &fermionic partner. These solve huge problems associated with the Higgs mass since the positive contribution by a boson is exactly canceled out by the negative component of the supersymmetric fermion partner. One might expect partners to have similar masses but it's a broken symmetry which results in SUSY particles being far more massive than the standard partner.
The problem is that no SUSY particle has ever between observed.  It's a likeable construct. It's thought that the least massive one would be the partner of the top quark, the stop squark. That ought to be detectable by the upgraded LHC, but we would want more than that. The SSC would have been a better tool for this purpose.