We were based in just outside Stirling and used PSS who gave a brilliant service. Although not Edinburgh based, they travel the UK doing specific export packing, which is done to a completely different standard than your normal house move.
Pickfords did not even make our short list. Have used them twice domestically. First time brilliant, second time awful...so did not give them the opportunity.
As has been said many times you go with your gut feel, so get three or so to quote and then see how you feel.
Important considerations
Can they pack the container and seal at your house? You then have complete visibility of the process. If based in Edinburgh you will probably ship out of Grangemouth.
Openness about the charges from MAF and what us involved this side.
What they are willing to take? Some people are told no out door stuff etc. but we cleaned and took everything.
Good Luck