To vinpous & Devieus:
While some theory books do suggest a convention of 3/4 being 3 impulses and 3/8 being one, in practice it hasn't been consistently adhered to that consistently in the literature (the classic Beethoven 9 Scherzo example comes to mind). Where the aural equivalence between 3/4 and 6/8 would lie would be in 3/4 with 2 bar hypermeter at twice the tempo of the 6/8, but not when the span of 3/4 is the same as that of the 6/8 bar, then they are not equivalent. The the hyper meter and the compound meter are only notationally different. There are some who will make the claim that the different notations would yield different performances, but that's edging into the territory of pseudo-science.

Then there's all the fun of hemiolas and polymeters (multiple perceived meters). Then metrical dissonance. Then Brahms. Some stuff in between. Then Ferneyhough broke music (in a good way). And now? The Python, Lilypond and LaTex don't want to play nice and give me my damn A1 sized score in 21 different meters at once. Bleh. Sod it, I'll just curl up and Netflix all the old shows I loved as a teenager because life's all too hard.

But seriously, this paper might be of interest:
Cohn, Richard, Theory of Musical Meter, November 2015, Yale University/University of Sydney
if you can get ahold of it... I might still have a copy somewhere.

It provides a pretty good first principles definition of meter and pretty good way of thinking about it, though limited after a certain point (damn it Ferneyhough), it could be useful within the scope of this discussion. What's nice about it is that it shifts the focus towards the aurally perceived time events.