We've moved three times (and I've moved twice on my own before that) and have always thought the packers/removal men are better at handling and packing fragile stuff than we would be! We've had no breakages at all. They are very very experienced and will ball up wrapping paper around fragile items. They are also expert at judging what will fit in what box which helps keep things safe and have boxes sized so they fit well into the van so it's packed tight.
They do move FAST. It took four men ten hours to pack up our house but they did a lot of that in one day, leaving us with a 'basic set up' overnight before the move day. They then came and finished the packing that day, then loaded the vans. If we hadn't used them we'd have been falling over boxes for weeks doing it ourselves - and it would have take a lot longer than 40 hours!
They have specialist packing stuff too - so the wardrobe boxes have a hanging rail, so stuff comes straight out of wardrobe, hangs in box, straight out again at the other end. Ours had special padded bag things for pictures and a giant bag thing for mattresses. Most of ours have moved chest of drawers, filing cabinets etc as they are - so with clothes in drawers, then just slotted back in. The most recent move they didn't do this and emptied all the drawers into boxes which was a bit of a pain to sort out. Ours also took apart a bed and a large wardrobe to get them to fit, unplumbed and replumbed in at the destination the dishwasher and washing machine. It's all stuff that makes your life a bit easier.
Declutter as much as you can in advance and eat up as much food as possible - they'll wrap and pack any tins etc still in cupboards!
The only things we packed ourselves and put in the car were a couple of suitcases to cover us for a few nights whilst we unpacked, some toys/kid essentials and a box of financial documents, passports etc. Keep your keys with you otherwise they might get packed!
They will pack and label boxes as the house is that you're moving FROM so eg boxes will be labelled 'living room - ornaments', 'hallway - coats and shoes'. If the house you're moving to has a very different set up of bedrooms/living rooms it's worth having a think about what stuff you might want to group together so it gets packed together.
Good luck!