6/4 or 6/8 should be impossible to distinguish by ear. The main reason for choosing one over the other is tempo - if there are quick notes they are easier to recognise in the longer note values of 6/4 than in 6/8. In both, the main beat is a dotted note value that divides into 3 equal notes. This gives the lilting feel (it's called a compound time signature).
In 3/4 each beat divides into 2 notes (called simple time). It should in theory be very different- 6 should be a 2 in a bar feel - more like a lilting 2/4 than a 3/4.
But... there are many pieces could be in 6, but are written in 3 (because each beat of 3 can start to feel like it is a separate bar).
So a lot of this comes down to feel or function (e.g. is it a particular dance form) which is informed again by tempo, but the other main aids are phrase length and rate / pattern of chord change.
If you start to feel that the shape of the melody works over 2 bars of 3 - then consider whether it should be a single bar of 6. If you feel that the melody really needs 16 bars to get through a basic statement, then maybe it should be 8 bars of 6.
On the other hand if the chords are regularly changing every 3 notes (1 beat of the 6/4 or 6/8, or a whole bar of 3/4) then maybe it should be in 3.
And some of it is down to rhythmic cells (patterns of note values)- going back a long way we used to have rhythmic modes - like we have pitch modes. These modes carried a signature mood that was understood. I suspect that some of that still survives today. For me, the rhythm of dotted quaver, semiquaver, quaver - or the 6/4 version of dotted crotchet, quaver, crotchet (the rhythm that sounds like 'Amsterdam') belongs in the compound time signature world rather than in 3.
