"Neural networks" vs. "Not neural networks" is a completely wrong way to look at the problem.

For one thing, there are very different algorithms lumped under the title "neural networks". For example Boltzmann machines and feedforward networks are both called "neural networks" but IMO it's more because it's a fashionable name than because of actual similarity in how they work.

More importantly, the really significant distinction is making progress by trail and error vs. making progress by theoretical understanding. The goal of AI safety research should be shifting the balance towards the second option, since the second option is much more likely to yield results that are predictable and satisfy provable guarantees. In this context I believe MIRI correctly identified multiple important problems (logical uncertainty, decision theory, naturalized induction, Vingean reflection). I am mildly skeptical about the attempts to attack these problems using formal logic, but the approaches based on complexity theory and statistical learning theory that I'm pursuing seem completely compatible with various machine learning techniques including ANNs.