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A song in 3/8 is typically twice as fast as a song in 3/4, so what is the difference from doubling the BPM?
EDIT: I am aware of the difference between 3/8 and 3/4, but then what is the difference between a quaver played in a piece with a certain BPM and a crotchet played in a piece with double that BPM?
It's probably more to do with the style or feel of the piece. Often a 3/8 piece would be in 1 whereas a 3/4 one would feel in 3 but that's a generalization. You can of course have a slow piece in 3/8 and a fast one in 3/4. Bottom line is there is no real difference between the two time signatures.
There is no difference between the two examples you give. It would be to do with convenience when writing it out.
It's by no means a given that 3/8 will be twice as fast as 3/4. There are some pretty slow 3/8 movements in the classical repertoire and plenty of fast waltzes written in 3/4. You are correct, a quaver in 3/8 at [dotted crotchet=60], will be the same length as a crotchet in 3/4 at [crotchet=180].
There have been various conventions regarding whether to choose 3/4 or 3/8 over the ages. They were never particularly rigid, and musical scholars delight in arguing over them :-)
