One way to prevent the problem in the future is to grant privileges to roles, then grant roles to the users. One way around the current problem would be to generate a script to grant the privileges to the new user. Something like:

set heading off feedback off [etc.]
spool grant_newuser.sql

select 'grant '||privilege||' to user_two;'
from dba_sys_privs
where grantee = 'user_one';

spool off
@grant_newuser.sql


Tim