Intaglio,
If you want to know what's most secure, i'd say a session would be as there is no data left behind when the user stops using the site.
If you want to know what's more professional, i'd say cookies would be as the USER does not see the difference between the two. The only difference they notice is that, when programmed correctly, when cookies are used the user won't have to retype several notes such as their login name or password. To make this more secure you can put in a "time limiter", allowing the cookie only to be usefull within a given time period.
I hope this helps,
Paul