I've seen this debate come up quite a few times over the years, and been involved in debates over it, as well. Now, I'd like to know your opinions on it.
As for myself, I am a proponent of dual sticks.
You may argue that it is unnatural, cumbersome, and slow, but I believe the opposite to be true for one main reason: I've shot real firearms before, including pistols, revolvers, shotguns, submachine guns (semi-automatic), and rifles, and a dual stick configuration captures that feeling of handling a real firearm much, much better than pointing and clicking.
With the point & click system, you can unnaturally swing a gun around as fast as you can move the mouse and focus your sights directly at your target(s) with the utmost ease. After shooting real firearms, that's just not how it works. Holding a real firearm fatigues you, of course, especially after holding it for an extended period (sometimes just going through one 15 round magazine can make you need to set the firearm down, depending on its weight and length... and if you're standing up). Applying force to the firearm to acquire multiple targets quickly is especially exhausting and it takes a bit of time to acquire them and take the shot safely and efficiently. Some PC setups make the firearm feel as if it's a plastic NERF toy... as if it weighs about a pound or so and that you can wave it around wildly.
A dual stick configuration captures the "heavy" feeling nicely and transcribes the real handling of a firearm very nicely. I like the slower, more predictable feeling of dual sticks. I can slowly adjust my aim and the screen follows where the firearm is pointing (as if you're aiming down the sights) unlike some PC (or even Wii) setups that angle the barrel of the firearm itself to where your mouse is pointing instead of both the player character and firearm as one unit.
One big thing (that is a bit unrelated to the topic at hand) is using an inverted aiming setup. Many N64 games had an inverted setup, and that's just what I was automatically used to and have used since then. People think I'm crazy for going inverted, but at the same time, I think people who use up/up & down/down aiming are crazy.
I like to use this visualization: Split a firearm in half (length-wise). The buttstock (yes, they're called buttstocks) would represent the right analog stick. Keeping that in mind, if the gun spins on the axis where it was split, pulling the right stick down (the buttstock) would make the opposite end (the barrel) point up, similar to a see-saw/teeter-totter/whatever you like to call those. I'll include an image to help you visualize it:
EDIT: So what are your opinions on the matter at hand and the inversion vs. "normal" debate?