Oracle Consulting - Strictly Consulting or Flexible ?
Stritctly Consulting means you will be sent to the client site as individual consultant or as a member of team to do database administration activities at the client site. Travel is mandatory.

Product Supoort consulting means you will be working for Oracle products specialization and you will be asked to find the resolutions which can't be supported thru world wide tech support.

Be specific in asking the kinda role and responsibilities Oracle will be offering you and make sure that what you wanted to do.

Think of Job satisfaction first and reputation later. Its my personal experience. Its the Question of where you feel job satisfaction and where you are happy, not how big is your Corporation.