Aren't these equivalent, given that the /proc/x/environ file exists?
Though I feel like in any modern app deployment scenario that isn't going to be a meaningful defensible boundary.
The answer is to use neither, especially given the number of times I've used a path traversal vulnerability to expose /proc/self/environ on a pentest, and the one time I was frustrated on a pentest when every app in the environment used a dedicated API for secret retrieval and the path traversal vulnerability I had access to was worthless.
There's a lot of bad advice on secret storage that is Not Based On A Threat Model™