A single result tells you where a group landed. A comparison tells you what moved them, and that is usually the decision you are actually trying to make.
Why one field
Change the price and the wording at the same time, and a difference in the result cannot be assigned to either. Change only the price, and it can.
This sounds obvious and is routinely violated, because it is tempting to improve two things at once while you are in there. The discipline is worth keeping: a comparison where one thing moved gives you an attributable answer, and a comparison where three did gives you a number nobody can act on.
What to vary
Date. The same population, the same question, two moments. What two years did to an attitude, or whether a norm has settled.
Scenario. The change you are testing: a price cut, a new pack, a rival's move, a different message. The most common comparison in practice.
Question. Rarely useful for a finding, occasionally useful for checking that a result is not an artefact of your wording. If two reasonable phrasings give different answers, that is worth knowing before you present either.
Population. The same decision put to two groups — your customers and the wider market, buyers and lapsed. Strictly this is a different kind of comparison, since both sides are equally "real"; there is no control.
Action space. Adding an option to see where its share comes from. Read this one carefully: adding an option changes the denominator for everything else, so every share moves whether or not anything real did.
What is held constant
Everything you did not change, including the parts you did not choose. All sides of a comparison run against the same environment and the same version of the same population, so the background cannot drift between them.
This is why comparisons are more trustworthy than their individual results. Both sides carry the same uncertainties, so the uncertainties largely cancel, and the difference between them is on firmer ground than either number alone.
Reading one
You get the two distributions side by side, the change in each option's share with a range around the change, and the reasons that appeared on one side and not the other.
The reasons are the part to read. A price cut that moves five points is a number. A price cut that moves five points and introduces "it makes me wonder what was wrong with it" as a new rationale is a decision.
A difference whose range crosses zero has not been established. The direction may still be worth noting, but do not present the size of it.
A practical pattern
Run the base case. Read the twins until the population feels right and the rationales make sense. Then vary one thing at a time from that base — three or four variants against the same base is a study, and it costs about as much as running four separate simulations while telling you considerably more.