I'm not really an expert when it comes to quadcopters, I heard about the "plus" and "cross" configurations and that the "cross" configuration provides more stability. I would appreciate any sort of help on the advantages and disadvantages of those configurations and the physics/maths behind why one is better than the other.
According to this paper:
pitch and roll control authority is up to about 30% greater for the cross-conﬁguration since all four (as opposed to only two) rotors are used.
However this is a bit academic as you often combine pitch and roll in normal flying, or fly at an angle, so it only matters if you want to do the fastest possible flips or rolls.
For most FPV people, the main advantage is that the camera can look out between the front two rotors. A lot of the time you're flying at an angle anyway (because you're looking where you're going while cornering), so the theoretical differences are minor.
Practically speaking, "plus" blocks the camera and has a different flight characteristic, especially when landing as you can drag a single arm if not "flat" and the chance of using the arms to level out is more difficult.
A big disadvantage is how a plus crashes. A plus design generally will be arm first and will not crumble like an "X" might. I don't fly plus because my crashes would be so much worse (50+mph cartwheels, fences, buildings, you name it)
I agree with @Robin Bennet, but that point is also moot in many scenario, especially FPV as the power to weight ratio is intense. I have 5 inch drones that legitimately rotate in excess of 1000 degrees per second on pitch and roll.
The flight controller will need to know of the configuration of course.
Another advantage of "X" over plus is the rotational nature of the propellers. I use a reversed spin. (see image, credit https://blog.seidel-philipp.de/)
By using reversed direction I am able to fly through grass and trees better because the props push debris away (not pull them in). Two props in the front pushing out has saved me from certain crash very often. I switched about 3 years ago and I can say that recovery from bumps is vastly improved. I also note easier take off as well from a lawn, less instance of things getting tangled, plus my camera lenses are not chipped as much from sand reflections and ingestion because the props work more actively to not throw junk into the drone, prop-wash notwithstanding.
In the end it is a preference, there are mild advantages to both but most to lean towards X for performance and logistical reasons. I see plus format very infrequently, usually someone experimenting. I hope that helps.