Joe,
ANR are very good at cutting out background noise, better than any passive set will ever be ... so for people such as your other half, an ANR set should help them focus on what they need to listen to rather than trying to distinguish against background noise that creeps in.
I do see where you're coming from on the budget side of things ... I guess there are two options, second hand ANR or an "expensive" passive headset for someone .... which is likely to be cheaper than an ANR set but still give better protection than a cheapie.
Up to you in the end ....your cash, not mine.