You're thinking too much in terms of the notes used (as in the names of the notes), and it's fooling you into thinking that these progressions are very similar. But it's really all about thinking in intervals, not in notes.
People make the same conceptual error all the time with modes: thinking about them too much in terms of note names, i.e. in terms of relativity to other modes, when really, outside of major/relative minor flips within a song, they aren't usually applied in the real world by moving between relative modes. They're normally applied as fixed variants on the typical major and minor interval patterns. It's best to think of them with a fixed root, and as different set of intervals based on that root. For example, people often say, "When you're playing in E mixolydian, you're just playing in A major." That is false. The notes happen to be the same, but in real world use, it's completely meaningless that they happen to be the same. If you play in A major over E mixolydian, you will be phrasing and resolving very, very differently, and it will likely sound terrible. You'll never make that conceptual mistake if you simply throw note names and modal relativity out the window, and think only in terms of modes being alternate sets of intervals based on the same root.
Quite honestly, outside of starting a song in its proper key, I haven't actually thought a note name on the bass (or guitar) in over 30 years, since I was a very early beginner – no joke. Once I get going with the song, my thinking is 100 percent about intervals/patterns: I, IV, V, bVI, b3, b7 = finger here, finger there. Not C, F, G, A, Eb, Bb, etc. Not only can you transpose anything instantly that way, with zero struggle, but things like similar alphabetical notes within different progressions (like you are taking about) are impossible to get confused.
In other words, it doesn't help you at all in the real world to think that I-IV-V in one key are the same note names as V-I-II in another key. There's very little application for that realization. What you really need to know is where to put your fingers for I-IV-V and V-I-II (as examples) in any key that is called, regardless of what the notes are named.