Yep...that covers both ends of the argument pretty well! I'll just add to Roger's point that with P&S cameras, you are viewing the electronic image direct from the sensor, transmitted to either the electronic viewfinder or LCD screen - so though you are not actually looking through the lens glass at the scene, you are looking at what the sensor is seeing. What are the plusses and minuses of that?
Well, looking through the lens itself, as with an SLR, you have much better optical clarity, can see in low light situations as well as you could with the naked eye, and can more easily track or follow a moving object as you are not subject to slow refresh rates of an electronic screen, display lag, overexposure whiting out the screen temporarily, etc. It's just your eye, through glass, to the object. Better, right?
Well, the argument for the P&S method is that by viewing what the sensor sees right on the LCD screen, you can actually see the output of your photo, the way it will look when viewing on your computer, before you even snap the picture. Adjustments to shutter speed, aperture, white balance, ISO, or EV are all made right on the live view. If your shot is going to be underexposed two stops, you'll see the darker image on screen. If your white balance is too cool, you'll see the blueish tint on screen. ISO too high? You'll see the overexposure right on screen. Since the sensor is the device capturing the digital image, seeing what it sees will help you get the settings right up front.
The argument can run in favor of both methods - and indeed neither is 'right' or 'wrong'. But much depends on your skill, knowledge, style of shooting, and personal preference. A person intimately familiar with their camera and how it responds at various aperture/shutter combinations can nail the exposure without having to see it on a screen - so they would rather have the big, bright, accurate viewfinder looking through the lens for clear focus and low light capability. A person not as instinctual with the settings, who tinkers alot to get it right, might actually be better served with a live-view camera that allows the sensor's image to be seen after all the processing and camera setting parameters have been applied.
And sometimes, it's just simply more convenient to have that P&S style live view! For example, taking a slow shutter night shot on a tripod...especially when the tripod isn't sitting straight at eye level. Having to bend over, looking through a little window, choosing all your settings, then firing off some slow shutter shots isn't as convenient as standing comfortably looking at a big 3" LCD, tilted up to point at your face, and seeing when you've got the exposure nailed at the right aperture for the shutter you want to use.
There is one more small advantage to P&S cameras that can occasionally come in handy - they can perform in absolute silence. A through-the-lens DSLR will always take a picture with a big, fat noise - as the mirror slaps up when the shutter triggers. Usually, that won't matter - but occasionally, a person snapping a pic at a golf tourney or in a classical music performance may get in some trouble with that noise. A P&S camera is all electronic - it imitates a shutter-like noise digitally...but an option in the menu can turn it off, and you can fire off all the shots you want in complete silence.
I've been a long-time P&S user (an ultra-zoom camera), and have had wonderful experience with it. I recently bought a DSLR specifically because I wanted the advantages that it can deliver in focus speed, burst speed, tracking focus accuracy, and high-ISO performance. But I did choose a hybrid DSLR which also has a live view ability. I use it with the viewfinder in the traditional manner probably 90% of the time - but having a big, tiltable LCD and the live view ability has allowed me to take some slow shutter shots, some above-the-head shots, and some on-the-ground shots that would have required me to perform an acrobatics routine to get without live view. Even if it's only 10% of the time...those few times it came in very handy - and I'm happy to see the line blurring between P&S and DSLR cameras! I love my DSLR, and still have love for my P&S cams.
