Remeber that the circle of 5ths/4ths has absolutely nothing to do with actual chords. It is just keys and notes. Here is how i look at each circle:
The circle of 5ths is used to show how many sharps or flats are in each key. It is like a clock. You start at the top with C that has no sharps or flats. Then you move clockwise (to the right) to G, which has 1 sharp, then to D, which has 2 sharps, then to A, which has 3 sharps, then to E, which has 4 sharps, then to B, which has 5 shaprs, then to F#, which has 6 sharps, then to C#, which has 7 sharps. From there, you switch to flats with Cb, which has 7 flats, then to Gb, which has 6 flats, then to Db which has 5 flats, then to Ab, which has 4 flats, then to Eb, which has 3 flats, then to Bb, which has 2 flats, then to F, which has 1 flat, then you are back at C. Here is an illustration:
C = 0 sharps or flats
G = 1 sharp (F#)
D = 2 sharps (F#, C#)
A = 3 sharps (F#, C#, G#)
E = 4 sharps (F#, C#, G#, D#)
B = 5 sharps (F#, C#, G#, D#, A#)
F# = 6 sharps (F#, C#, G#, D#, A#, E#)
C# = 7 shaprs (F#, C#, G#, D#, A#, E#, B#)
(switch)
Cb = 7 flats (Bb, Eb, Ab, Db, Gb, Cb, Fb)
Gb = 6 flats (Bb, Eb, Ab, Db, Gb, Cb)
Db = 5 flats (Bb, Eb, Ab, Db, Gb)
Ab = 4 flats (Bb, Eb, Ab, Db)
Eb = 3 flats (Bb, Eb, Ab)
Bb = 2 flats (Bb, Eb)
F = 1 flat (Bb)
C = 0 sharps or flats
The circle of 4ths is where your progressions come from. In other words, it has solely to do with bass/LH notes. To me, that is the only significance of it. Just take the circle of 5ths and read it backwards.
See what I mean by keys and note? Circle of 5ths is for keys and circle of 4ths is for notes.