Difference between fixed and folding blade knives for skinning is subjective. More or less up to the user which is better.

Here's how I feel about knives:

I have both, use both. I generally keep fixed blade knives in my fur shed, since they're a bit easier cleaning. For my pack knives (i.e. knives I skin in the field with, and keep in my pack), I keep folding knives, mostly to store and haul them more securely.

Fixed blades are easier to clean and often a little lighter weight than a similar sized folder. Fixed blades can often have blades longer than the handle, whereas getting more length out of a folder means having a longer handle, more weight, more bulk.

Folding blade knives are nice to just throw in a pack or pocket. Blood, fur, fat, etc gets plugged down into the blade groove, so plan on extra diligence to clean that out.

Don't get caught up in long bladed "hunting knives" for skinning either. You'll only ever use a few inches of blade for skinning small game & predators, so no sense in handling 10" of extra weight.

I prefer about 4" of a nicely curved blade, preferably a drop point or straight back blade. Lightweight, good grip, and high quality steel. Up to you whether you use a 'skin hook' version or not. I don't really like hooks on a folder, since it inevitably snags on stuff, but on a fixed blade, it can be nice.

The Gerber knives I have now are just fine (7-8yrs old?). They're plenty cheap, rubber scales, and hold an edge nicely. Kershaw makes fairly affordable knives as well, I've use a Kershaw "Blade-Trader" for about 15yrs, ordered several extra blades years ago, have only had to have the grip replaced on warranty once as the unit wallered too much and the blades got 'wobbly'. I just picked up a Buck Knives "Omni" fixed blade, figure I'll get another one soon after I get to see how it holds an edge.