Recently I had a discussion in which it was pronounced very confidently that anyone who didn't think Bach's music showed more contrapuntal independence than Perotin's was crazy. In fact, it was suggested that such a person did not exist. My immediate thought was that since the lines in Bach's fugues were derived from the same melody, they weren't particularly independent. At least Perotin has different melodies in each part. Is this an outrageous suggestion? To someone trained thoroughly in the "common practice" style, perhaps it is. The original, anonymous person was incredulous. The comparison makes a good starting point for the present discussion, in which I want to consider what makes for "independent" counterpoint, and how that might impact questions of quality or musicality.
When it comes to pondering notions such as contrapuntal independence, especially when the people using the terms are so obviously conditioned by particular musical styles, one starting point is to take the words at face value and consider what they imply. For "contrapuntal" I'll take the simple idea that the music should be conceived as individual musical lines, rather than as chords or the like. To be as independent as possible suggests that those lines should have nothing to do with each other. Now, clearly, most music isn't like that. The lines are related in various ways, and that's basically the idea of counterpoint per se. As a point of discussion, we could construct "maximum independence" by selecting melodies from various world traditions and just playing them all at once at random paces. Well, the latter is easier said than done, but we could do them all in separate recordings. Some of the more difficult modern classical styles attempt vaguely similar things, with lines which are barely related or which actually incorporate random elements. Still, for true independence, collage is the way to go. I don't think that is really what people have in mind when they talk about making contrapuntal lines independent.
It is also natural to ask how complicated the individual lines are on their own. In this case, it was suggested that Bach has more rhythmic variety, and is therefore more complex (as a vague synonym for contrapuntal independence). This is not so clear to me. Yes, Bach employs a greater variety of rhythmic notation, but his music is also put into the guise of 4/4 (or variant) bar-line time with its regular beats. When it comes to Perotin, maybe "rhythmic" is not the correct word to apply to music without regular beats, but that is the best we can do for this dimension. The music employs subtle rhythmic relationships, with poetic slurs, and a general flexibility of meter (or at least this is how I believe it should be performed). It has fewer rhythmic symbols available, but in some ways I think it is more complex rhythmically... it is less regular, and correspondingly more subtle. Both Bach & Perotin go on to relate their individual lines in clear ways. In Perotin's case, as noted, there are distinct melodies in each part, with the most important ones moving at different speeds. Rhythmic motion in lower parts dictates the framework upon which the upper parts are superimposed, so the lines are highly related in this way and not especially independent when compared to our collage example. They are also related harmonically by regular cadential formulas. In Bach's case, the cadential formulas and harmonic relationships are even more regular as a part of standard tonality (about which my previous thoughts are especially disjointed and in need of elaboration), and of course the lines of the fugue have the same melody. There are many specific relationships, and again the lines are not especially independent. One might pretend to answer the question of "complexity" by asking how easy it would be to memorize a comparable length piece by each, but this would clearly be a joke on the Bach lover, since familiarity facilitates memorization tremendously.
The described discussion actually originated in a dispute over whether the interval of the fifth was "impossible" for independent counterpoint. Perotin uses it regularly, and seems like a good counterexample, at least for someone willing to let other styles have some weight in the discussion. It was admitted that fifths were fine in Bach et al., as long as they weren't between "chord tones," whatever that means (joke!). I think those statements amply demonstrate how style-dependent such pronouncements are. An issue related to independence is whether the lines are roughly equal in significance. This wasn't mentioned, and I question whether it is really implied, but it's an interesting topic nonetheless. It is clearly not true of Perotin, whereas it is the heart of fugue as a texture. (I might also note that our collage example can also be constructed so that this is true, trivially so.) The fugue balances the difficulty of apprehending equal lines by using the same melodies throughout. In other words, it sacrifices independence to make a more balanced texture, and of course Bach does this in particularly stimulating ways. The idea has its obvious predecessor in the pervasive imitation of Josquin Desprez, his peers and followers. The strict style did not last long for vocal music, but was adopted enthusiastically in the instrumental domain, where it made its roundabout way to Bach. Within this particular domain, I would say that Gombert's textures are rather more complicated than Bach's, both because they frequently employ more individual lines and because they have fewer harmonic constraints.
If Gombert employs the most complex fugal textures, there are other Renaissance examples of similar level. Beyond that, there is still the question of imitation, or of reusing melodic material in each line. Free counterpoint is much more impressive to me, and of course the era from Machaut to Josquin employed it in a variety of contexts. I start with Machaut and the Ars Nova notation simply because rhythmic ambiguity is dismissed by some people, and in the fourteenth century we can have e.g. explicit syncopation at least as elaborate as that which Bach employed. If we want to consider only equality of line, then we can discard cantus firmus technique (perhaps), and still be left with a large number of works with apparently equal voices. Some of Machaut's isorhythmic movements are of this type, as are many of Dufay's. By Dufay's time cantus firmus technique was so advanced, that it would be difficult not to say that those are his most impressive contrapuntal works. Ockeghem takes all the techniques of the time to the next level by employing them without a cantus firmus. For me, the height of counterpoint per se is in the great works of Ockeghem and his contemporaries, prior to the emergence of widespread pervasive imitation. We are perhaps too conditioned to view the fugue as the end-all of counterpoint, but free counterpoint has many exciting ideas besides passing a melody from one voice to another. The key element to appraising quality in these works is the degree to which the music carries its momentum forward from rest to climax and beyond, with the lesser works frequently yielding to a static malaise. This is where Ockeghem particularly excels, and it is precisely the feeling that each voice contributes fully to the forward momentum which yields the notion of contrapuntal independence.