Does fat as opposed to oil distribute flavour better?
Saturation doesn't effect the extraction or distribution of flavors, your beef stew was just more flavorful than your chicken stew. Any fat (and that includes oil) will do the job, the difference is in the flavor of the fat and texture differences you would get from the different oils. Beef fat will be richer than olive oil, giving the impression of flavor distribution when it's actually the amount of flavor that is different.