This topic is current for me as a consulting assignment to a multi-national company here in Kuala Lumpur, Malaysia, nevertheless the outplacement services covered here, are equally as relevant just about anywhere around.
Essentially outplacement happens any company has determined a requirement to retrench a quantity of employees, but rather than only terminate their employment, with minimum redundancy payment as required by law, they recognise a certain responsibility towards those who will suffer their jobs.
There are of course, many reasons for jobs becoming redundant (and in almost all jurisdictions, the law mandates that it is jobs tend to be being lost) with the resulting retrenchment of opportunities report holders, if they simply cannot be redeployed within the boss. The company I am now working with on an outplacement assignment has sold one of its divisions to another company, as well as the buyer does not want the employees.
In my view, and that various HR pros, if you have experienced retrenchment yourself, you won't be truly effective being a counsellor to an agent who has just been told they are losing their job. An early colleague once compared it to outplacement advice childbirth! She commented that unless you've given birth, you cannot possibly empathise! While somewhat extreme, I have to agree :-) The whole consultants involved in outplacement (me included) have all been retrenched at skill and have a psychology or counselling certification.
In some cases, your former company will pay to make a change and use the firm of your choice, providing the cost is the same. Contact the human resources department, let them know you're unhappy with the agency, and that you would like to find a substitute.
If the company won't allow to enjoy a swap, see if they'll contact the designated firm on your behalf, indicating that you'll be displeased. If enough individuals are dissatisfied with the service and make your former employer associated with it, that become an impetus so they can contract with another agency. You won't know if do not have to try.
As a last resort, you may opt to go with the tab for outplacement services in your own. It'll be money well spent if at the same time you find an occupation more quickly.