To measure the gasket thickness you need a caliper, digital calipers can be had from harbor freight for $12.99. They also are needed for checking your squish.
https://www.harborfreight.com/4-in-digital-caliper-63710.html
Your squish will easily tell you if a head is increasing compression (to some extent). All you need to do is pull the plug with the head/gasket installed, take a length of solder and insert it far enough that your at the outer edge of the piston (make sure your not in a transfer, intake or exhaust port as that will cut the solder) then slowly turn the motor over by turning the rear wheel. This will crush the solder, measure the thinnest point and this is your squish band.
A good range to be in for performance seems to be 0.7mm +/- 0.1mm. You don't want to go much below this as metal expands with heating and you need to ensure that you can accommodate it. This is why you can buy copper head gaskets in thicknesses like .2mm, .4mm, etc. Personally my build has a 0.75-0.8mm squish with a roughly .5mm head gasket and I want to try a .4mm to bring the squish down to the roughly .65mm range. This is with a CDH "high compression" head that seems to have the same amount of compression as a stock head.
Compare the squish of both heads, you'll probably find the head that has less power to have a larger squish.