You have an old DNS server: tallboy.example.org
You have a new DNS server: ns1.example.org
You have a domain, example.com, for which you want to swap the old DNS server with the new DNS using nsupdate.
NOTE: the domain is example.com
The NS servers are in example.org (different domains).
These are the commands you issue:
update delete example.com. IN NS tallboy.example.org. update add example.com. 3600 IN NS ns1.example.org. send
Of note, you mention the domain first, the NS server second.
This took me a while to figure out tonight.
You will also want to update the records with your domain registrar.