I got quotes from PSS, Anglo Pacific, Crown and Pickfords.
Crown couldn't figure out where we were moving from and to. The quote came as Leeds to Auckland, then was hurriedly corrected to London to Auckland. Trouble is we were moving to Christchurch. I didn't trust them to actually get it righ when it counted, so they were out.
PSS attitude intrigued me, they were big into slamming other companies service. I didn't like that as a pitch, but still asked them to quote and requote.
Anglo Pacific came in much more expensive and wouldn't negotiate.
So we landed up with Pickfords, as their quote was middle-of-the-road and they seemed fine. It landed up being a bit of a mixed bag. The packers were polite, efficient and seemed very competent. Their office support, however, was abysmal: the "move manager" went AWOL with no email out of office or phone forwarding; two days before we flew, which was 2 weeks after packing, we still didn't have confirmation of when they would be shipping our kit (it transpired it had already gone, and they hadn't told us this- or the vessel name, as promised.) ; they didn't refund for variation between packed and quotes volumes...we spotted the difference on the delivery note and had to follow up twice before they repaid the cash as they said they would; and we had a book case and chest of drawers obliterated, and a sofabed damaged.
I have heard of many more people who had great Pickfords experiences, though. So I think it just goes to show you- so much depends on who you speak to, who you get as a "move manager", and what crew turns up on the day. Do your research, go with who you trust most and get a good vibe from.