Isolated Flyback vs Isolated Buck Voltage converter. What are the Pros and Cons?
I've generally only seen people use fly-bucks where they don't care too much about output regulation, but care more about cost.
Flybucks are smaller and simpler because they do regulation on the primary side since the secondary tracks the primary side relatively closely.
Flybacks actually regulate the output and require control to cross the isolation barrier. They also have large voltage spikes that are intrinsic to the design and require snubbing. This increase in complication gives you more precise regulation, meaning you can use it at higher power levels.
More reading here: https://www.ti.com/lit/an/snva674b/snva674b.pdf
For your specific case, if ease of implementation is most important, then you want fly-buck, but at near 20W of power, you are probably going to get not great regulation (if that's what you mean by stability), but flybuck will be cheaper as it doesn't require isolated control nor snubbing.