Double butted spokes are, for a given weight, stronger.
Also, as they are a higher grade product, they may be made from stronger materials.
Traditionally, the problem with stainless spokes is that they’re a bit more brittle, however this is no longer a problem with the grades of stainless now available.
You’d have a problem with corrosion on even a rustless spoke before you had a fatigue problem on a well built wheel in any case (fatigue only comes into play if the spokes are too loose, never quite got my head around why a spoke going in and out of tension is worse than one having a varying amount of tension above zero, but have proved it to myself through lazyness on hack bikes…)
Anyway, for the ultimate in strength, as someone has already said, go for triple butted.
Lacing, wheel build, spoke count and the rim strength will make far more difference though in any case. Plus you can always end up dinging the rim on a rock etc.
In the OP’s situation, I’d go for it using DT competitions. Have found Sapim’s not as good, and some other brands way inferior.