My company paid for my move this summer. I moved like 60 miles from where I use to live in a shared 2 bedroom campus apartment. I owned NO FURNITURE. As in, I had clothes, books, kitchen stuff, tools, and a bike. Two guys from an Atlas Van Lines contractor showed up in a truck (about the size of a medium u-haul) and ate up 4 hours packing every single thing I own in paper. Can of soda-wrap it in paper. Can of corn-wrap it in paper. Plastic cup-wrap it in paper. Garden hose-wrap it in paper.
Nothing broke, and it made packing the stuff into boxes easier for them, so I guess I see the point... but it took forever! My company paid for a "full pack and unpack". I asked the guys to just put the boxes in my new place and let me unpack myself.
I saw the estimate for what my company paid. It was nearly $3000! I felt bad about that. If I had know it would cost the company so much, I would have rented a truck and done it myself.
I told one of my co-workers and he was shocked. He moved about 20 miles to his new house last year. He's got a kid and a wife and regular furniture (beds, sectional couch, etc.). He says he was estimated $600 and paid $800. I imagine he packed everything himself and was just paying for the move.
Shop around.
Good luck.