Quads: very stable, but slow to deploy and very awkward to set up in thick vegetation or on slopes. Difficult to track a moving animal, and doubly so if using in deep vegetation (heather, bracken, brambles etc). Best used when you have time to set up, and are on clear, level ground. But the stability is almost as good as off a bipod.
Twins: quick, easy to deploy and much less difficult to use on slopes or in vegetation. Easy to track moving animals. But definitely less stable and much more affected by wind pushing you about.
I have both and now swap back and forth depending on context.