FYI, I made the change from a UK host to a US host.
It was a co.uk domain name, so I changed the host via nominet.org.uk instead of via the existing host, just in case the existing host played the devil with the account during the changeover, such as throttling back the bandwidth.
When the host is changed, not all of the domain name servers change the location of the new host's server at the same time. It can take two or more weeks before all of the domain name servers are up to date, so it is advisable to activate the site with the new host while keeping the account with the old host going.
In that way, you don't lose any visitors, as you would if you cancelled the old host's account, which some domain name servers will be listing as the host until their lists are updated - sometime several weeks after the host has been changed.
I did not lose any visitors and my search-engine ranking appears to have been unaffected.