The competing values are freedom and equality at all times. Conservatives tend to favor freedom and are willing to accept inequalities of outcome from a free market. Liberals tend to favor equality of outcome and are willing to sacrifice and circumscribe freedom in order to get it.
i think this accurately describes the nature of the debate in our country, but the problem is it assumes that freedom and inequality can coexist or that vice versa, freedom and equality cannot coexist.
All of this ultimately depends on how we define freedom. American independence (freedom) is at its roots freedom from british rule, also perhaps freedom from being ruled by any other nation-state. However, when we occupy Iraq at least in part to "spread freedom" it doesn't occur to us that people living in Iraq may not want to feel as though they are being ruled by us. Nor, in our commitment to free-market economy, do we consider that we are bound to and limited by our need to endlessly grow the economy. And perhaps most troublesome is in our freedom, how often is inequality the result of not being free from sin, the cruelest master of all. Regardless of policy, sin is often what stands in the way. Trickle down economics may make sense academically, but it will never work if the people at the top believe their freedom is to keep as much as they want, making the trickle a very slow drip. Likewise many social programs are in good heart, but may be abused by some who believe their freedom entitles them to work the system rather than use it to get their life together.
For me the question is not a balance between freedom and equality, but one about the source and nature of freedom.