Relative performance is how people who design and use supercomputers define them. Cost is a secondary effect because if you're going to shoot for the limits of what we can do, it's going to be expensive.
The major difficulty with your second list is that expensive computers don't need to be high performance. Consider the computers that go into satellites and spacecraft. They are extremely expensive, but not high performing.
Here's a simple test.
Suppose that I give you these two measurements:
SPECmark: 1.2 million.
SPECmark: 3 million.
Which one is the supercomputer? Without knowing the date, there's simply no way for you to tell.
Suppose instead I write:
System cost: $20 million 1990 dollars
System cost: $400 1990 dollars
Which one is the supercomputer? I think most people will be able to pick which one is which.