That is an interesting poll question. On the one hand, the Vaults are unquestionably safer, you have non-irradiated food and water so no gradual radiation poisoning or mutation, alot lower chance of being murdered (though some vaults did descend into chaos and rebellion with people being killed inside). You also have considerably more comfort and luxury, ability to shower daily, a tv and a radio and a pip-boy you can play basic video games on, etc. On the other hand though, most of the vaults were designed as science experiments, some of them quite awful. There is also a pretty large lacking of freedom with your job being decided for you by your GOAT test results and strict marriage rules to preserve genetic integrity.
As for the wasteland, you have alot more freedom, but you have very obvious risks, most food and water is irradiated, mutated wasteland creatures everywhere (some of them like Deathclaws very dangerous), raiders, cannibals. Showers/baths seem fairly uncommon because purified water is too rare to waste on bathing, and nobody wants to regularly bathe in irradiated water sources, so most people are grungy and likely smell pretty bad, so sex is going to be pretty awful.
So I guess ultimately the choice boils down to which you favor more, freedom or safety/easy living. I think ultimately most will pick safety and easy living over freedom, we see this even in the real world, and the Fallout example is skewed even more heavily in favor of safety/comfort over freedom than in most real world examples. That explains why Vault life is winning in the poll by quite a large margin.
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