I've done it both ways. I wish I could tell you that
one way is clearly cheaper than the other, but it
really depends on different factors. What I usually
do is pull out the ol' notebook and hit the internet.
I jot down the prices from the hotel websites and
the airline websites then hit the package websites.
I've gotten great deals with a package and sometimes
I've gotten better deals by shopping around. and, of
course, sometimes I've found a great deal and gone
back a day to two later to find it over and gone. But
sometimes my hesitation has resulted in big savings.
Too bad there isn't just that one, magic answer, isn't
it? I'd use the cheaper one every time!