Let me add my two paise here. I have owned over two dozen cameras. Currently I own two Canon, two Nikon, two Panasonic and one Ricoh cameras. Apart from these current ones, I have owned everything from Hotshot to Nikon D3, film to digital, 1/2.7 to APS-C to large format. With that background, here goes my two cents.
High end compacts come with a very short term feel-good factor. I had Panasonic LX3 and LX5, both acclaimed enthusiast cameras. I have to say, I would have been very happy with them had I not used DSLR before. But since I bought those as "always carry" camera side-by-side my main cameras (DSLRs), I was disappointed. They leave a lot to be desired when it comes to the "entire photography experience". If all you ever need is a "good camera" for family photos (either for sharing online or printing up to 6x8 / 8x10), you would be very happy with compacts.
A DSLR camera on the other hand, comes with a photography experience which is incomparable even to the best of compacts. It's a very potent tool, which sets only sky as the limit. But....
But DSLRs are not for everyone. It is easy to buy an expensive camera and still take a lot of bad photos. Just because the user can't utilize the qualities of camera. I feel more comfortable with my D90 than with my D3. Why? Because I have owned D90 for much longer. It's lighter, more manageable. I am used to the controls and can set it up for a shot literally blind folded. Working with D90, my hands will reach the right controls even in dark. D3 on the other hand is a very elaborate camera and much more complicated machine. It also happens to be the more expensive and more capable of the two. But if I am in a hurry to take a shot, I pick the D90, because of the aforementioned reasons. With the D90, I am more likely to get a better shot quickly than D3.
The same can happen to a first time DSLR user. By the time he will set up his DSLR, he could have missed that shot which wasn't meant to last till he set up his camera. In such a case, a compact which powers on in a fraction of a second, focuses fast and gets you the shot is the camera to own. Many people (most people in fact) buy a DSLR and use it as a point-n-shoot. Why? Because, they either don't have the necessary skills, or the time, or both, to deal with the complexity of a DSLR.
So, what should you buy? A compact or a DSLR? Keep in mind, advanced compacts these days come with DSLR like flexibility and entry level DSLRs come with point-n-shoot like ease. So whichever way you go, you can get the sophistication you want, the ease you want. Only, the extent will differ.
To sum up, a DSLR will give you (1) ultimate in control (2) satisfaction of photography (3) space to hone your photography skills and rediscover things based on your personal philosophies. Be warned, however, that a DSLR will also bring you unwanted attention. Many people will suspect your motive and you will sense people around you becoming conscious about your presence (your DSLR rather). Warning #2, a DSLR may also open up a new avenue of expenses. Once you get into it, it's a lot of expenses. Lenses, filters, bags, lights, stands. Warning #3, be ready to get in shape. A good DSLR with a good lens might weigh around 1.5 Kg and will test the strength of your arms in anything but a short casual session.
A compact will allow you to remain more mortal among your family and friends. Will give you decent enough picture quality for general use. In fact, once you learn to utilize your compact well, you can even produce stunning photos with them.
In case you choose to go with a DSLR; buy one that fits well in your hands, feels good to you and comes in your price bracket. Among DSLRs, my top choice is Nikon. Biggest advantage with Nikon is that Nikon kit lenses are freaking good. You don't "need" to upgrade from Nikon kit lenses, until you decide to spend significantly more.
In case you choose to go with a compact, choose one with a fast start up and fast focusing. If the two criteria are not met, the whole point of a compact camera is lost. Among compacts, my top choice is Sony Nex.