I am confused between these two time signatures. What is the difference really. I can listen to a hymn in 3/2 time and i can see how easily I can replace the halves with quarters and the quarters with eighths, slow down the tempo, and it will sound the same. I find it confusing with other times signatures as well.
3/2 time gives the impression of a slower piece. 3/4 is 'normal' (whatever that is!) and 3/8 gives the impression that the piece is quicker. Only because three minims, being 'longer' notes, take twice as long to play as three crotchets. Obviously at the same bpm/tempo. But - play 3/2 at 150bpm, and it's the same end product as playing 3/4 at 75bpm.
So, effectivly, there's little to no difference. 3/2 will look a lot less cluttered on the page, possibly easier to read, and because the 'notes are longer', will give the impression that it's going to be slower than the same written in 3/4. It's an illusion!
To be honest, there's no real difference. I believe old hymn notation used half-notes a lot more than nowadays. Perhaps it was easier to write in the old days of quills, as minims (full notes) are easier to "draw" than the more complicated notes with stems( i.e. crochets/quarter notes, quavers/eigth notes, etc.). Potentially 3/2 gives the reader an impression of a more formal, stately feel, than a 3/4 would.
The modern approach is to use precise tempos in bpm in which case 3/2 and 3/4 can be exactly equal by just changing the bpm and playing 3/2 twice as fast to become the same as 3/4.
Traditionally, before metronomes, note values were an indicator of tempo. Rhythms with longer values were performed at slower tempos. So 3/2 would be a slower tempo that 3/4. For a written source you can check Rameau's Treatise on Harmony. I'm sure there are other sources, but that's a good one.