OK, I did try to google it and couldn't pin it down.

As near as I can make out "tacche" is notches and it's either 6 of them or 3 of them.

Huh?

 

Precisely.

 

Perhaps positions of adjustment?

 

Yip, "Sei Tacche" refers to 6 notches and "trei tacche" refers to 3 notches on the caseback.

Am I correct in saying that the trei tacche is more rare/valuable?

 

Certain Sei Tacche references such as the 6111 (Big Indian) and 23086 (13ZN12) are extremely rare/valuable. However, the average Tre Tacche is generally more desirable than the equivalent Sei Tacche. This is largely due to the Tre's case design with its attractive stepped bezel. Here is some information on the Tre Tacche: http://www.longinespassion.it/Longines_Passion/Tre_tacche.html

 

Ah! It's pretty obvious now. Thanks!

 

And Thanks for the link @DirtyDozen12 .