It is a huge dilemma moving hosts or servers. The biggest issue is the Mysql databases. What is the best way to make a back up of a mysql databases where it will work on all servers regardless of mysql or php version.
SHELL by a wide wide margin! serjio28 is right. The more closely you can control --and monitor-- the process, the better off you'll be.
it really depends... even though ssh is the best... phpMyAdmin dump can be pretty good when it's a small database and not much data.. i've tried to dump big databases via phpMyAdmin and it was just not happening.
phpMyAdmin is only for small sites, you'll almost always have to become acustomed to actually using ssh