DSLRs are more demanding and require a certain amount of skill.
But when you know how to handle them, they can help you get stunning results. But DSLRs are really only for people who take it seriously and are willing to devote some time. Otherwise the results you get are not considerably better than the ones you get from the average point and shoot. Maybe even worse.
I can personally recommend the Nikon D40 as a great, easy to use, "newbie-friendly" DSLR. It is pretty cheap as well(over here a kit with a decent lense is about 500 euros) and provides excellent value. Don't bother getting the D40x though, its not worth the extra cash.
One thing you always have to consider with DSLRs though are the additional costs. Often there is a good kit lens that comes with the camera but for certain situations you might want to get other lenses which can be quite expensive too. also you will need to get proper SD or flash cards (depending on the camera), as DSLRs usually save the images in RaW format, which is considerably larger than jpeg and alike.
But DSLRs are a lot of fun if you are into photography. also you are usually treated with more respect as DSLRs look way more professional than normal digi cams with integrated lenses. Therefore you look way more professional too.
regards