well, AFAIK generally difference between those fittings are that brabs are less restrictive coz they have larger throughput ( if i can call it so) but i dont think that difference is noticable. another difference is that comp fittings are more secure coz they are compressing the tube ( squeezing it onto an inlet) and of course theres an aesthetic side of things as well coz you dont have to use clips/worm drives.
Barbs are more popular coz till recent compression fittings were only available for 8/6mm, 10/8mm and 3/8" ID - 1/2" OD tubing only but now there are all sorts of compression fittings including 1/2" ID - 3/4" OD tubing ( and thats the thickest available tubing). Of course there's also compability side of things where ie. some chipset or MOSFET blocks have the intles to close to each other and that doesnt allow you to put compression fittings on them ( they are too thick)
Yeah only pro version of everest shows you all those temps.