What I can see, is that the main difference is not about "SHA1" but about the certificate chain. See the icons. Both "SHA1" messages are locked with a green icon, but the part about about the identity of the website is different.
GOOD: *.mail.live.com . Certification owned by Microsoft, verified by Symantec Class 3.
According to digicert.com, no error or warning was found in the certificate. Not sure why no warning is displayed about the use of "SHA1".
Issuer: (Extended Validation : EV)
- Symantec Class 3 EV SSL CA - G3
- VeriSign Class 3 Public Primary Certification Authority - G5
BAD: outlook.live.com . Certification owned and verified by Microsoft. Probably the certificate is not correctly set or recognized by Chrome (see issuer).
According to digicert.com, it found 1 warning: SSL Certificate uses a deprecated signature hash
.
Issuer: (Organizationally Validated: OV)
- Microsoft IT SSL SHA1
- Baltimore CyberTrust Root
So I strongly think that there is a small recognition problem of the chain issued by Microsoft itself.