The main reasons for using SWFObject that spring to mind:
EOLAS patent - this was important a couple of years ago as it led to annoying "click to activate" messages in Internet Explorer, but the legal case has been settled and this is no longer a problem.
Validation - the EMBED tag is not valid, but you may not care (it still works).
Detection - SWFObject detects whether the client has the requisite Flash player and allows for easy use of alternate content if it does not.
Search Engines - the alternate content can be read and indexed by search engines.
During the EOLAS dispute I had to change a huge number of pages from OBJECT/EMBED to SWFObject, and I have never seen any reason to go back.
In your case, providing embedding code to others would seem reasonable, though even in these post-YouTube days a surprising number of people do not have Flash installed (and actively dislike it).