I love all that kind of stuff!
I too have both Bungeed and Skydived! Bungee 2 Skydive 3.
WordMan’s post describe my sentiments and experience pretty well!
I did the static line jump, I didn’t want to be strapped to anyone! Anyhow the
rules, at the place I went, were that you had to be able to get into that
skydivers position, the X face down, twice in a row, before the static line
pulled your ripcord (5 seconds to do this) before you could free fall on your own and pull your own cord. All three times I was a spinning ball, happy though, till the static cored pull my chute! Oh, the grand view floating down 
I did the Bungee later on in life and like WordMan said I could wave at my brother on the
ground, scream at him ect. It was much more “Real.” You think wow look at how high I am,
and about to Jump. My left leg start twitching uncontrollably the first time. I took a deep breath, calmed my self down, then jumped and went best ride you can have! Weeeeeee!
Skydiving the view before jumping is more surreal!
Also, IMHO, I think that somewhere in the back of my mind the reasoning was …
Skydiving … proven technology … since W.W.II … especially learning, they use the
W.W.II paratrooper type chute. Round. They just ask you, make sure your not to
heavy or light for the chute. Oh, they teach you how to land correctly. Feet togeather.
Bungee, newer technology, they have to weigh you, know the elasticity of the
cord, jump height, do the math correctly, and makes sure you jump from a safe place
so you don’t hit the point you jumped off on the way back up! Seems like more could go wrong!
As for that “feeling” you get … like other posters said … I really don’t feel it …
just for a sec maybe. Your mind is really too busy with other stuff… trying to
orient you in free fall! And in my case having fun!