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This dichotomy between background dependent and independent theories is sometimes traced back as far as the antagonism between Newton and Leibniz about absolute vs. relational space. Most physicists would claim that the choice of approach is merely philosophical so far as no different falsifiable claims follow, not unlike the question of interpretations of quantum mechanics. However, two philosophers of science, Imre Lakatos and Elie Zahar, have argued that research programs can be driven by metaphysical questions and so adopting the view of background independence may lead to different results.
This is not a suggestion that spacetime is uniform, merely that the fundamental rules governing the measurable characteristics of the physical universe are the same everywhere, at all times.
One of the major shortcomings of loop quantum gravity is that, as of 2009, it has not been shown that the theory in fact reduces to Einstein's general relativity in the continuum limit. Since GR equations were used initially to construct the theory, many researchers assume that they can be recovered, but this has neither been explicitly proved nor disproved. In addition, incorporating matter into the theory is an ongoing problem.
Assume pure gravity first. Say we have two coordinate systems, x-coordinates and y-coordinates. General covariance demands the equations of motion have the same form in both coordinate systems, that is, we have exactly the same differential equation to solve in both coordinate systems, except in one the independent variable is x and in the other it is y. Once we find a metric function gab(x) that solves the EOM in the x-coordinates we immediately know (by exactly the same reasoning as above!) that the same function written as a function of y solves the EOM in the y-coordinates. As both metric functions have the same functional form but belong to different coordinate systems, they impose different spacetime geometries. Thus we have generated a second distinct solution!
Although the physics of string theory can in principle be background-independent, perturbative formulations of this theory do not make this independence manifest because they require starting with a particular solution and performing a perturbative expansion about this background. Non-perturbative formulations such as matrix theory and AdS/CFT resolve that issue and are fully background independent.

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