We are in a migration process of a group of related computers (Intranet servers, SQL, application servers of one application) to a new domain. In the past we used one domain user account for every computer (web1, web2, appserver1, appserver2, sql1, sqlbackup ...) to access central Windows resources like network shares. Every computer also has a local user account with the same name.
I am not sure if this is necessary, or if it would be easier to configure and maintain to use one domain user account.
Are there key advantages / disadvantages of having one single user account vs. dedicated accounts per computer for this group of background servers? If I am not wrong, one advantage besides easier administration of the user account could be that moving installed applications and services around between the computers does not require a check of the access rights anymore. (Except where IP addresses or ports are used)
I might be misreading what you're asking here, but if you have one domain, then your domain administrator account will have admin rights on all of the attached systems.
The only advantage to creating multiple, separate accounts is for partitioning of responsibilities and control. One separate admin account for each server might make sense if each server had its own administrator and you wanted to ensure they didn't overstep their responsibilities.
As for local users, it's wise to maintain separate accounts on each member server that you can use should your domain spontaneously explode, but I wouldn't say there's any need to use them for day-to-day administration.