How to best move sites to other servers?

[xciso]

Hello.
I am going to set up a new VPS so it is fresh and up to date with all softwares.

Which will be best?
Set up a new VPS with new ip adress and copy everything over from the old.
And then change from the new ip to the old server have.

Or..
Set up a new VPS with new ip adress and copy everything over from the old.
And then change the nameserver for the domains to the new ip's.

Or can i do it on a better way?
I will have so litte downtime as possible. I have full ispconfig, with mail-server, http-server, ftp-server, dns-server..

Thanks!

[falko]

I'd change the IP - this will have less downtime than changing DNS records because it can take up to a few days until DNS changes propagate over the internet.

[xciso]

Thanks Falko!