I've used several over the years moving all over the country. FWIW, my worst experience was from Two Men and a Truck out of the PA/WV area as they "lost" (stole) more than they delivered.
Ironically though, from NC back to OH I was forced to use Two Men and a Truck again and it was a good experience. After talking to that crew, the supervisor advised me they usually just subcontract based on the area. His advice was to just get one that has great documentation practices and their insurance covers based on that documentation not a generic coverage policy. He also highly urged that anything not easily replaceable always move yourself or it is very likely to disappear.
We had a group from Allied Movers that took me from Dayton OH to PA/WV and they packed everything up, before closing the boxes had us sign off on the contents then they sealed it shut. We had to sign off on the tape with a sharpie along with the packer. This was the best i'd ever seen and everything single thing arrived. They left no window for anything to disappear.
I've also read decent reviews about places that subcontract college kids to come in and box stuff up for you. You just have a moving van show up, the same college kids will load the truck up then meet you at the destination and carry all the boxes back into the new place. Many use a similar packing procedure where you sign off. If you have any questions shoot me a PM and i'll give you my cell.