InMail vs. LinkedIn Message: Communicating with a 1st Degree Connection

As the title suggests, when reaching out to a 1st degree connection on LinkedIn, InMails come at no cost. But is there any real benefit to using an InMail instead of a standard LinkedIn message in these situations?

Ultimately, which option is more likely to capture their attention? I’m curious to know how the user experience differs between the two.

For context, my primary focus is on headhunting, so making a memorable impression is essential.