If it's not a fast ride and you'll be stopping a lot it doesn't sound like the speed factor of a road bike is much of an issue. In which case, either bike sounds like it would be fine for this ride. If your commuter has upright bars and is set up for urban riding I can't see why it wouldn't be preferred for this ride. Drop bars are great for speed but are not always best for riding in a city with a group.

Also, my concern would be which bike would be at greater risk of theft or vandalism during all those stops. I ride in NYC but do so on my folder or on my hybrid commuter my road bike isn't my first choice here.