IMO.....It's mostly personal thing.......Kind of like a single reed duck call vs a double reed call.
The double reed would be the slate. It's a little easier to use and has a surface that needs a little less conditioning....And the sound is very hen sounding.
The single reed has characteristics of the crystal/glass......A little harder to use, but has a more ringing/sharper sound. Hence, it has a little more volume for longer distances.
Both calls are good and most every turkey hunter I know carry both. If I was only going to get one, I would get the glass.....There's tons of decent low cost slates out there that sound just fine (think DR-85 duck call)......2 cents
ps.....Remember, the striker makes a big difference in the sound and ease of using the call.....The boys at Hook's will match the striker to your call for you.