InMail vs LinkedIn Message to a 1st Degree Connection

As the title suggests, when reaching out to a 1st degree connection on LinkedIn, InMails are free. But is there a benefit to using InMail instead of a standard LinkedIn message for this purpose?

Essentially, which option is more likely to capture their attention? I’m curious about the differences in how each method is perceived.

For some context, I primarily focus on headhunting and need to ensure that my approach stands out.