InMail vs. LinkedIn Message to a 1st Degree Connection

As the title suggests, when reaching out to a first-degree connection on LinkedIn, InMails come at no cost. But is there any benefit to using an InMail instead of a regular LinkedIn message for a first contact?

The key question is which method is more effective at capturing their attention. I’m curious about the differences in their user experience as well.

For context, I primarily work in headhunting and need to ensure my outreach stands out.