I truly do not understand the difference between 6/8 and 3/4. 6/8 just sounds like two bars of waltz. The emphasis is the same. I suspect the key lies in understanding the second part of the signature, the 4 and the 8. What I gathered from discussion about metronome issues above is the 8 and four are just quarter or eighth notes, so it seems like semantics whether you choose 3/4 or 6/8? Since two bars that have three beats and three quarter beats sounds identical to a bar which has six beats and six eighth beats? There must be some further distinction that only becomes apparent with more complicated musical stuff happening.
Experience of playing songs in those time signatures will help it become real and not abstract. With that experience, listening to songs in those time signatures becomes revealing.
Here are a few videos:
6/8 vs 3/4 https://www.youtube.com/watch?v=dsD9M7aIA5E
What’s the difference … https://www.youtube.com/watch?v=N4q2kBe82-o&t
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These were really helpful in clearing up my confusion, thanks Richard. 
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