The data above is from Openbuild’s GT3 page.
Upgrading from 6mm GT2 to 9mm GT2 you get x1.5 (or 50% more) engagement.
Upgrading from 6mm GT2 to 6mm GT3 you get x2.35 (or 135% more) engagement.
Going with GT3 means you also need to change the default $100 & $101 to accommodate for the new pitch.
This has been also discussed here: