I think the one, big advantage of the pass is that it allows you to control a card (as said before : middle to top, middle to bottom, etc...) or a group of cards (which I'm not sure is possible with the side steal) in a split second, while appearing to do nothing at all. It's as simple as that.
Let me tell you how I discovered that I really needed to learn the pass : there's an effect in DGP1 called "Satisfaction garanteed", a great all back routine. The moment that really sells the effect and make people truely believe that indeed, there are just double backers in the deck, is when you put their card in the middle, just a snap of the fingers and boom, it's on top. That's when people say "okay, not impressive at all as there are all the same". In the explanation, DG says that you can also double undercut the card, but to me it doesn't sell as well the illusion, because they can think it MIGHT be the same card as you cut the deck a couple of times. With the pass, they clearly see their card in the middle, and then you turn the top card immediatly, so it CAN'T be theirs. It's soooo much more magical !
I knew that the side steal would allow me to do that, but as the pass has more applications, allows you to control multiple cards and can be made invisible (no matter what people say), I went or it...and I use it all the time, it's my favorite control ! Quick, smooth, invisible...What more could you ask for ? The main downside is that I can't perform it well enough while sitting, which can be a big problem if you mostly perform seated at a table.
To finish, the DVD that really allowed me to understand the move, its mechanics and psychology is "Pass with Care", there's in it all you need to know to learn a good, practical pass. (unlike Ninja 1 I must say...). The important thing is not to learn 4 or 5 different passes. Learn well 1 way that you feel comfortable with -maybe 2 with the turnover pass- and you'll be fine !