Everything they do differently is irrelevant as long as the user is asking them to do those things. If Gmail starts showing me fetish porn that's bad, if a fetish porn site does the same thing it's fine.
The only relevant difference is security/privacy, in which Google may be more trustworthy but even that is debatable, regardless of which side of the debate you land on.
LinkedIn: moving their content to your e-mail address.
G-mail/Yahoo: Duplicating your content.
LinkedIn: Manipulating your content.
G-mail/Yahoo: E-mail providers.
LinkedIn: Social media provider.
G-mail/Yahoo: uses protocols as intended to provide service.
LinkedIn: uses hacks to provide service.
G-mail/Yahoo: No risk of compromising devices.
LinkedIn: Extreme risk of device compromise. Intentionally circumvents device security features. Multiple potential points of security breach (at proxy server, at web server, through rendering engine).
No comparison, really.