I just moved from Central to New Territories, both apartments with lifts but on high floors. Hired a moving company and the whole thing took about 3.5 hours and cost $3,200. We have a 3bdrm place that was full - about 15 pieces of furniture and 30 boxes of stuff I think. 4 pieces of furniture had to be dismantled and reconstructed at the other end. We packed all our stuff into the boxes they delivered before the move except the kitchen - I left that to them to pack. Not a single thing was lost, damaged or broken.
We put all our stuff into storage before moving to HK and it took a week to do. Never again will I try and move myself.
I highly recommend the company we used and chose them after someone else recommended them on this site. They were quick with the communication, quote by the piece (I sent them pictures and estimated the number of boxes) and the guys on the day were an hour late but all go once they arrived.
The website of the company we used was http://www.ika.com.hk/index.html
Why not get a quote just to see if it is much more than the cost of the van rental and the hassle of sourcing the boxes.