It might help to look at the Greek that the translators see when they look at this verse:
13:7 ἀπόδοτε πᾶσιν τὰς ὀφειλάς τῷ τὸν φόρον τὸν φόρον τῷ τὸ τέλος τὸ τέλος τῷ τὸν φόβον τὸν φόβον τῷ τὴν τιμὴν τὴν τιμήν
Believe it or not, each of the highlighted words are a single entry in the Strong's dictionary:
1) this, that, these, etc.
So each item that is owed is owed individually. I may owe taxes to the various levels of government, revenue to the people who work for me, respect to the people I work for, and honor to those people who deserve honor. Those categories may or may not overlap. The ESV is clearly the more faithful to the way the Greek is structured.
On the other hand, the strong parallel structure combined with the cultural assumptions of Paul's audience and the immediate context show he intended all of these things to be owed to those in authority. In the Psalms and in Paul's writing, heavily parallel phrases are meant to draw a line of equivalence between two or more concepts. For instance, earlier in the letter Paul writes:
And those whom he predestined he also called, and those whom he called he also justified, and those whom he justified he also glorified.—Romans 8:30 (ESV)
In this case, it's a bit more clear that the same people are referred to in each clause. But the strong repetition of "and those whom ... he also ..." reinforces the connection. In Romans 13:7 it is possible that the parallel could be pointing to the principle of owing what is owed. However, in Roman culture, far more than our own, people forged powerful, hierarchical relationships with each other. Reading the rest of the letter, a Roman citizen might be assume that the patronage relationship Paul described between Jesus and the church might supplant the human relationships. This verse contradicts that misunderstanding.
And, of course, Paul uses the entire section starting with Romans 12:3 to make his point that we should not use the revolutionary work of Jesus on the cross to attempt to climb the social ladder. Paul reaffirms the philosophical notion of the chain of being, but asserts that God governs even the top human authorities. We don't have to leave our current network of obligations because ultimately God is in control of even our political processes.