Separated at Birth?
Both approach scripture as if it is a scientifically provable proposition, where the only way it can be true and authentic is if it is empirically correct and without internal tensions or disagreement. All of the little irrelevant errors and disagreements that literal inerrancy is doctrinally compelled to justify are proclaimed "evidence" of the falsehood of scripture by atheists. They parade them around with all the sophomoric smugness of a blog debater who thinks that pointing out a misspelling is a great rhetorical triumph.
That demand that scripture's validity be empirical and mechanistic in nature reflects the most dangerous flaw in the doctrine of literal inerrancy. That flaw manifests itself in another parallel between fundamentalism and atheism. When presented with the assertion that Holy Scripture derives it's authority from the presence of the Holy Spirit, both literalism and atheism respond dismissively: "Well, that's just totally subjective. You can't prove that! Holy Spirit? Hah! No it's not! More like your own overactive imagination. Why...then scripture could mean anything! If it's not literally infallible, then it can't be trusted."
At least the atheists are aware that they're committing the unforgivable sin.
The very heart of the Reformation and the reason that Scripture was raised up to counteract the idolatry of ecclesiastical inerrancy was that Scripture finds it's real authority in the presence of God's Spirit. As articulated by John Calvin in his Institutes of the Christian Religion (Institutes, Ch.7, Section V), for scripture to be Holy Scripture requires that it be read with eyes and a heart that are guided by the illumination of God's indwelling Spirit. It is the interplay between the inspiration that guided the authors and editors of Scripture and the Holy Spirit moving in one's own spirit that gives the Bible it's authority.
To argue that the Bible derives it's authority elsewhere, and that it governs our lives as faithful Christians because it is verifiably determined to be without error by a series of logical proofs utterly and blasphemously misrepresents the foundation of it's authority.
Not that I have an opinion on the subject.