@OP, I think my use of the Comparator may differ from how you are using it. I am using as a means of comparing my handloads to a reference cartridge. That reference is often a hand loaded cartridge itself. And depending if the rounds will be fired from a magazine I may NOT use the Comparator at all.
Key point: The Comparator is mostly useful when comparing the SAME bullet used in multiple cartridges. Generally, do not use it to compare different bullets. Even two FMJ bullets from two different manufacturers do not have the same ogive so comparing them will result in different measurements.
Here are my reasons to use the Comparator...
Consistent case volume: Because of bullet tip malformations (see right two tips in the below pic) the COAL measurements alone will not tell you if two (identical) bullets are seated the same in two cartridges. This can be significant if your are near max charges. Seating the same bullet based on COAL will result in the bullet base being at at different heights within the case resulting in different available case volume for the powder charge. This means two cartridges with the same COAL will develop different pressures when fired even if the charges are identical. Using the Comparator you can ensure the length from case head to ogive is the same even of the COAL is different, providing more consistent case volumes which translates into consistent velocities.
Repeatable length when COAL is not critical: Except when you are at max allowable COAL for your magazine, you probably want to use the Comparator as your tool for comparing the length of completed cartridges. As shown above, the lack of consistent tip shapes can greatly affect the COAL measurements, but have no effect on the Comparator measurements. This allows a reference cartridge (or just the reference measurement from a reference cartridge) to be used to recreate the same Comparator length. Useful when you are constantly changing the seating die setting every time you change the bullet being loaded. Since buying my Comparator I still capture the COAL for my reloads but also capture the Comparator length and usually use it as my target to recreate the load.
Don't use Comparator when fitting a max length cartridge into a magazine. A few of my magazines strictly limits the COAL to 2.260". 2.262" COAL cartridges will usually jam in the magazine. As shown the variation in COAL can make consistency difficult with LEE dies. For these reloads the focus is not consistent volume in the case but rather not exceeding the COAL. The Comparator cannot tell you this. When loading heavy bullets that need to be loaded at 2.260", I use my calipers to make sure the COAL is 2.260" or slightly less, so the rounds don't get stuck in the magazine.