As a soil conditioner I prefer composts that are derived from leaves, woodchips, grass cuttings, etc. to manure products. But once they are well broken down it doesn’t make that much difference, although pH can be an issue. I actually buy composted yard waste from a site wholesale where the pH is higher than I would like, as I prefer something in the low to mid 6’s for brambles and most everything else, if only because raising pH is much easier than lowering it. The 7.5 pH of this stuff is perfect for fruit trees where the native soil is in the mid 5’s to mid 6’s though.
As far as your question, I don’t think the source is as important as the state of the product- how well composted it is, how it smells and how heavy it is. If there aren’t split open bags I’d test a bag of each and make my decision based on that.