For a pair of games I am working on, I'm trying to work in a VERY basic evolutionary timeline for a lot of the more mythical creatures to set up design language of some of the creatures. This timeline will give me an idea of which creatures are related to which in order to help guide the design process of each game world as I go forward. The two settings are very different, but have a similar problem that just have different means of getting to similar end results.
Winged quadrupeds are something that don't really exist in our world (some avian dinosaurs may have walked with their wings, but I don't count them as quadrupeds.) As has been pointed out in multiple questions on the topic of flying quadrupeds, evolving extra limbs is a very expensive and unlikely event. Having it happen multiple times for different animals would be even stranger.
So, instead of making each one have their own separate events where something evolved the extra pair of limbs, I thought I'd make it so they had a smaller number of evolutionary ancestors shared by multiple creatures that are similar enough (gryphons and hippogryphs and giving dragon-like creatures shared evolutionary ancestors, etc.)
For one of these game worlds, there will be centuries worth of strange magic saturating the world that will have the side-effect of speeding up evolution to the point of millions of years worth of evolution happening every century, so mutations like this are at least more likely for that one. Humans will have been in a magical slumber to hide from the effects of this magic, returning to find their world much different. The other game's setting is a far older planet than our Earth, having far more time for such creatures to evolve before intelligent life came to be.
Going down that path for the solution, would it be more likely/logical for a flightless quadruped to evolve extra limbs that would eventually become wings? Or for a bipedal flying creature to grow an extra pair of legs/claws?
I should note that I am looking for answers that work for both worlds. The magical side-effects mentioned for one of the worlds is more of a catalyst to speed things up so I can have humans wake from their slumber and still find some serviceable infrastructure among the ruins of the old world (though there will be some mutations that are strictly magic in nature like elemental imbuements, they are not relevant to this particular question.)
EDIT: I suppose a better way to ask this is which of the two body plans (bipedal avian or quadruped) would benefit more from the additional limbs/wings?