I don't really know either, I'm just pedentipointing out that the security of one of these things is an actual number, measurable in bits and this fact makes Aumasson's argument possible to begin with.
The 'security' of any program even in relatively constrained cases is woolier. Is a C program that can't write to executable memory at all but can allow the interpretation and execution of some language it happens to interpret vulnerable to RCE, etc. So if there is a parallel of some sort, it seems to me it could only be a narrative one.
Analysis of security of arbitrary programs is in its infancy, we can't quantify anything yet. I think the best we have is halvarflake's provable unexploitability [1] and that is very weak.
But I'm just noticing how many named cryptanalytic techniques, like Boomerang, Impossible Differential, even I guess to an extent Slide, are really extensions of Matsui and Biham and Shamir. And that's true of C/C++ software too: most attacks seen in the wild are derivatives of just a couple basic techniques ("out of bound write" is obviously putting my thumb on the scale, but "buffer overrun", "integer mishandling", and "use after free" cover a pretty good fraction of all attacks on memory safety).
Which is all to say: "we've had no good ideas since differential" might not be as meaningful as it sounds? Or maybe it is. Sometimes the best way to get good information into a message board thread is to add bad information, and, in theoretical cryptography, I contribute that ably!