Biggest single advantage (for me) to a DSLR is depth of field. Most if not all copacts are limited to a minimum f8. Some only f5.6. If you do any scenic or architectural photography, being unable to stop sown to f32 or even f16 is a real problm.
Being able to change the lens makes a dSLR extraordinarily versatile. With a superzoom camera you can't switch to a fast wide aperture lens for a narrow DOF to blur out your backgrounds or to an ultra-wide angle lens for sweeping landscapes or to a fisheye for funky distortion effects without using an image degrading add-on lens of dubious quality (adding extra glass will always degrade image quality).
DSLRs also let you use external flashes which can make a HUGE difference in your photos by giving you MUCH more flattering light.
There is no "supposed" to the superior image quality of a dSLR. The larger sensors show MUCH less noise and you can purchase lenses that are sharper and show much less optical abberations than a superzoom camera lens. If you're printing 4X6 snapshots and not agressively cropping your images then no, you might not see much of a difference at all. If you don't see any difference, there's no reason for you to consider a dSLR but I do large prints, crop very agressively and often shoot in VERY low light so there's no other choice than a large sensor camera like a dSLR for me. The right tool for the right job...
I recently bought a Nikon P100, and I like it a lot. It's light, easy to use, and very versatile. I love the zoom range; it's amazing -- none of my SLR lenses come close.
BUT -- It's not as sharp as an SLR lens. It's ultimately not as versatile -- for example, there's neither hot shoe nor PC cord socket, which makes it difficult to use with off-camera flash. I could use a slave triggered by the on-camera flash, but then I still have the light from the on-camera flash to deal with.
I don't currently have a DSLR. But I will be buying a D200 from a semi-pro photographer I know in a couple months, and I'll be able to use my older Nikon lenses with that. Then I can do most of what I want to do. (And that's when the P100 becomes mainly my girlfriend's camera -- she wants to learn photography, and it seems a great learner's camera.)
On the other hand, the P100 does shoot HD video, besides its general convenience and versatility. Bottom line: Each has its strengths. The super zoom doesn't replace the DSLR, but it complements it nicely, in a way a lesser point-and-shoot can't.
For me, the biggest difference is in the speed with which the camera does what you want it to do. Even the best compact cameras have a noticeable shutter lag--in other words, the time from when you press the button until the camera takes the picture. That doesn't matter if you're photographing something that stays still. But if you're photographing something that moves--for example, children, animals, sports events, the ocean--you rarely get the picture you intended to make. With a DSLR (or any SLR), there's virtually no shutter lag. Compact cameras also tend to have longer shot-to-shot times than DSLRs.
I've gotten many great images with my compact cameras, and I love the convenience of keeping one in my pocket or purse. But I'm almost always more satisfied with my picture-taking experience when I drag the DSLR along with me, even though I hate carrying it.
It is observable by real people like me. I have canon SX10, which is super zoom 20X. You can't even compare this more or less recent camera to my old horse DSLR Nikon D50. Quality of the image isn't simply there. DSLR is always producing better images than super zoom compact, always.
I have to agree with you Silicon Valley Girl. I love the extra long zoom cameras. I have a FujiFilm HS10, which goes to 720mm, and can go to f2.8 too. Amazing lens. Does great portraits.
But as you say, it takes much longer to record photos- 2 to 3 seconds per photo, as against almost instant for dslr. Also, the dslr has that shutter click, which makes you feel you have a "real" camera, as against the weak wimpy "dit" when the shutter goes off in a brridge camera.
Of course, if you need silence, the shutter is going to be a problem, but you know what I mean.
Adrian, I also have the Fiji FinePix HS10 which I settled on after using the Sony H50 and the Nikon P100. When sounds are unwelcome it's possible to silence the camera completely by pressing and holding the DISP/BACK button for a few seconds or selecting Silent Mode ON in the setup menu. And in situations where the single frame delay means you're likely to miss what you want you can use the Continuous Shooting mode which offers numerous frame choices in both RAW or RAW+JPG. Very useful I've found. I love this camera. But I've also discovered the Sony HX5 which is pretty incredible.
Consider your final use. I think we all need to really carefully consider what 80% of our photo taking will be and then buy the camera that best fits that need. For the other 20% (for me anyway), a compact point and shoot and a DSLR work. So, as the the old 80-20 rule applies, for me the best practical option is the P100.