Security difference(s) between Shamir's Secret Sharing Scheme and Blakley's Secret Sharing Scheme? We know that Blakley's scheme is less space-efficient than Shamir's and that they both work based on pretty different aspects (Shamir = polynomial-based; Blakley = hyperplane-based).
Looking at how both work, my gut feeling tells me Shamir’s scheme seems to be more robust than Blakley’s because – for example – if an insider can gain any more knowledge about the secret than an outsider can, then Blakley's system no longer has information theoretic security.

But gut feelings rarely tend to represent actual facts and I might be missing something in relation to Shamir’s scheme, which is why I’m asking:  Are there any practical security differences between Shamir's Secret Sharing Scheme and Blakley's Secret Sharing Scheme? Am I correct to think that Shamir’s scheme is more robust than Blakley’s?

It would be nice (but optional) if you could add one or more relevant references to your answer.
They are both perfectly (information theoretical) secure, as you mentioned, Shamir's Secret Sharing Scheme is more space efficient.
When Blakley's scheme is optimized by using finite fields, it eventually turns into Shamir's Secret Sharing Scheme.
They are equal from a security perspective.