IMHO one needs to use several different methods, if one wants to achieve a good, lucrative job in Dubai / Abu Dhabi / elsewhere in the Middle East.
1. Send your CV to the best Recruiting Agencies.
2. Apply directly to some Firms in your sector.
3. Contact all the people you know (whether or not they are in the same sector as you), because they may know someone who is.
4. Keep a tab on this excellent forum, as well as some other Gulf Expat forums.
5. Create a very good profile on LinkedIn, and, join a few 'job' groups on it.
6. 'Like' a few pages related to jobs on Facebook, such as
http://www.facebook.com/Dubai4everJobs7. 'Follow' a few influential recruiters on Twitter.
8. Use CV Distribution Services to send your CV to several hundred employers, in the Free Zones as well as the other parts of Dubai & the rest of the UAE.
You have to give it your 200% best. Just doing 1 or 2 methods won't give you the results you wish to achieve.
Hope This Helps!