A friend of mine told me that it does not make any sense to compare a entry level DSLR (e.g. Nikon D5100) to a super zoom (e.g. Nikon Coolpix P510).
So, what does he mean by "it does not make any sense"?
Comparing feature-by-feature is meaningless, a DLSR (even entry level) and a superzoom point and shoot are systems that choose almost opposite tradeoffs at every important design decision.
It's a bit like comparing a sports car and a mini van - while both are cars they are different systems designed for different purposes.
If the words small, light or cheap are high in your priority list you have no reason to look at DSLRs.
On the other hand, if you want to control how your photo looks no P&S in a the world will give you the power and flexibility of a DSLR (especially after you add another lens or two and an external flash).
Stop listening to him. You can compare anything you want. A DSLR and a superzoom? Sure. A DSLR and a cellphone? Yes. A camera and a fishing rod? Why not! You will see many people compare things which are quite different, even here on this site.
Think about the questions when someone asks if they should get a new lens or a new camera. What they are doing is comparing a lens to a camera. How? You have to establish a metric. When you decide between the lens and a camera, the metric is usually which will improve photography in some type of situation.
So, go ahead, pick a metric and compare them! Which will be more suitable for such and such type of photography? Which will give you more enjoyment per dollar? You is less likely to get noticed? etc.
The super zoom is a compact camera without (i) interchangeable lenses and (ii) optical viewfinder. On the other hand a DSLR, even an entry level one, will offer these two features (the reflex in the name has a meaning, after all... :-) ).
Usually (and for sure in the case of Nikon) this means that you can buy other lenses from the lineup of the compatible lenses (both by Nikon or by other brands), even "pro" lenses: and all of sudden you have an entry level DSLR camera body with a pro lens at your disposition.
Obviously one of the appeals of the Coolpix P510 is the super zoom lens (focal length from 24 to 1000 in 35mm equivalent). But this lens, as useful as it can be to have such a magnification available, will in any case imply a tradeoff (a huge one, at that!) to cover such an enormous range. It will have its more or less sweet spots, chromatic aberrations, distortions and so on. Furthermore, it will have a given range of minimum apertures (probably not so fast, even if f/3 at minimum length is remarkable). This is the tradeoff that you are accepting: in exchange for the comfort of not having to bring several lenses with you and the reduced weight, you are stuck with a single lens chosen for you, giving up the chance to choose the lens that you prefer, which could be as good as you like and your budget affords. Notice that a DSLR will probably not allow you to cover such a large focal length range with a single lens.
Each one of the two approaches has its merits and the choice between them is up to you. In my case, after having some point-and-shoot type of camera (possibly not as good as the P510) I decided to switch to a DSLR.
At last, to answer your question, having compared them right now I think that it is possible to compare a DSLR and a compact super zoom.
They are two different kind of camera.
Not to mention that reflex can cost up to several thousands of dollars.
Bottom line: superzoom are made to be small and to be sold to general public. Reflex are made to be good and to satisfy enthusiasts (or pros).
Somewhere in the middle you get things something like this.
It's not an SLR. But it does much the same job.
That's an 18-55 lens.
As it's a 24 megapixel camera you can crop the middle of the image down to 6mp and call it an 27 - 164mm equivalent.
Using 1/4 of the sensor it sill has more sensor area than any superzoom
120 x 67 x 43mm
353 grams with battery and card = 54% heavier than Pansonic SZ below 23.5 x 15.6mm sensor - area = 367 mm^2 24.3 mp
6.08 x 4.56 mm sensor area = 28 mm^2 =7.6% of NEX7. = 30.2% of 1/4 of NEX7 sensor.
103 x 60 x 33mm 229 grams
Could I fit a NEX-7 in my pocket?