Since I don’t think it makes sense to speak of the “surprise” associated with an improper distribution, I think the claim you want to make doesn’t cut to the heart of the matter. There are lots of reasons to object to improper priors, but this isn’t well-formed enough to be one of them.
Perhaps “better in every case” would work? That is, less surprising no matter what happens?
Since I don’t think it makes sense to speak of the “surprise” associated with an improper distribution, I think the claim you want to make doesn’t cut to the heart of the matter. There are lots of reasons to object to improper priors, but this isn’t well-formed enough to be one of them.