LibreSSL and openSSLRampage is the OpenBSD response, and, it's absolutely in keeping with their character. I admire the "Fuck it, let's just fix this shit" attitude that goes along with it.
The Core Infrastructure Initiative is the Linux Foundation's response.
They're two valid ways of dealing with the problem. the LibreSSL way is more direct, targetted, and, in a way, satisfying, especially if you run OpenBSD, and can gain from these efforts relatively quickly.
The "Core Infrastructure Initiative" is looking at it from a more holistic perspective and saying: OK, OpenSSL was in trouble and nobody noticed, what other projects are in the same situation, and how can we prevent what happened to OpenSSL from happening to other projects.
Neither way is necessarily "The only right way", or even better than the other way. In fact, both approaches complement each other. OpenBSD fixes the actual current problem child, Linux Foundation is on the hunt for the next problem child