It's better to drive to the trailhead in the other party's car, so that after each finishes the hike they can just go home in their own vehicles, and exchange keys later on. That way, if there are delays, nobody is stuck waiting at the meeting place.
It's a great system but can backfire if something goes wrong. I tried this with a Portland-area couple in the Wind Rivers. It would have worked fine except that my dog got sick and I had to abort my trip. I camped along the trail a few miles from the trailhead to rest the dog. The couple finished early and got by me without my seeing them, so when I got back to the trailhead, their vehicle was gone and they were halfway back to Oregon! I found someone who was going out who agreed to call the couple for me from Pinedale (no cell phone reception at the trailhead) and they sent the Great Outdoors Shop shuttle to rescue me.