Some (maybe not all) aspects are:
Insulation per weight ratio
While your observation "the thicker the warmer" is true in general, there are fleeces that are warmer for the same weight and thickness than others. Unfortunately, there's normally no objective measure given for that feature in product descriptions.
While simple fleece fabrics are built on a base fabric that does not stretch at all, more expensive ones are woven in a way that makes them stretch. This allows the clothes to be tailored more close-fittingly while it still can follow the wearer's movements. A more body-fitting jacket provides better insulation for the same fabric and saves on fabric and hence weight.
Cheap fleece fabrics are more susceptible to "pilling", i.e. the fibers tend to clump together into small spherical fuzz under repeated frictional load.
Cut and features
The cut of specialized alpine gear is typically optimized for this usage. For example, alpine clothing typically does not have seams on top of the shoulders pieces since they can be irritating or lead to chafing when wearing a heavy backpack. Since this construction requires more pieces of cloth and is harder to sew, cheaper jackets might opt for simpler constructions.
Also gear by more expensive and alpine-specialized brands may have nice features like pockets that are placed in a way that they are not blocked by your backpack straps, zippers that can be used with gloves and similar small advantages. It is not said, that a cheap piece of clothing won't have such features, but sometimes more by chance than by design.
Finally, you will of course also pay for the brand name on the more expensive gear.