Again, do a lot of reading about equal temperament to understand this phenomenon. In equal temperament, all 3rds and 6ths will "beat."
In the case of the first of your newest examples (which is in equal temperament), the fifth partial of the G almost--but-not-quite coincides with the second partial of the B. Since they don't quite coincide, you'll hear that rhythmic wobble in the resulting sonority. In piano tuning, we listen for and use that beat speed to decide how to tune intervals correctly. In this case, we would describe the beating as a 5:2 coincidence.
In your second recent example, you have lowered the B. Now, the fifth partial of the G almost perfectly coincides with the second partial of the B. Since the 5:2 coincidence partials match, you don't hear beating. This is the essence of just intonation.
In your third example, you are comparing the equal tempered upper B with the note that is an octave below it, a lower equal tempered B. In traditional practice, the first B was most likely tuned first, then the lower B was tuned to sound like a pleasing octave with it. So, of course they sound good together. (To be honest, as a piano tuner, the octave doesn't sound all that great to me, though it's acceptable).
Since you like the second example, you are discovering just intonation, and your preference for it. Again, to understand the drawbacks of it, tune the B as in the second example, then play a B major chord, and an E major chord. You'll discover that they sound terrible! So, in just intonation, some chords sound great, some sound kinda acceptable, and some sound terrible. You can mostly get away with using just intonation in simple music that doesn't use a wide palette of chords and doesn't modulate to other keys.
Equal temperament can be described as a system in which all like intervals (say, all major 3rds) sound either "equally good," or "equally bad," depending on one's perspective. They'll all have beating, and that beat speed will about double as you go up one octave (since an octave is a 2:1 frequency ratio). It's the most consistent tuning that we can do, since music in equal temperament sounds pretty much the same in all keys. That's it's advantage, and why it has been so widely adopted.