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Time

What 3/4 and 6/8 have in common is that they both allow for 6 eighth notes in a bar.Where they differ is that in 3/4,the eighth notes would be counted "One and Two and Three and" wheras in 6/8 They would be "One and a Two and a". In other words,in 3/4 you have 3 pairs of 2,and in 6/8 you have 2 groups of 3,so it has more of a triplet feel.
 
This generally means that 6/8 tends towards faster tempos - it is also used in Afro Cuban music a lot with groups of two bars. 3/4 is genrally a "straighter" feel as you mention - like a waltz, but obviously can be stretched and played about with in Jazz contexts. There is a Tommy Smith tune that is like a 12 bar blues, but has some bars in 3/4 and some in 4/4, making it feel very strange - like an 11 bar blues. Good one to lull cocky soloists into a false sense of security! ;)