A wide range of emotions - obviously joy at the birth, mixed with distress at seeing their mother in pain. I found the staff (first birth) to be generally rude and pompous with the exception of one midwife. I made a number of complaints about various incidents, but nothing was ever done nor any apologies given.
The second birth was a more pleasant experience, though it was a cesarean under anesthetic so I can't really speak for the mother. We chose a different hospital. The staff had a much better attitude there.
There was never any question about me attending the births, though her father couldn't quite get his head round it.