When ultimately deciding on which one to go with you have to account on more than just your initial purchase. Your putting your money into a system (body, lenses, flash, accessories, etc...)
For what your describing you want a new camera for, you'll definately need a few lenses. Maybe 3, maybe 2. Maybe more. Think of everything as tools. Everyone has a hammer and some screwdrivers, but for other jobs you need a circular saw, or jig saw, or table saw, or a jackhammer or sledgehammer or a compound miter saw. The more specific the tool needed for the job, the more expensive the tool becomes. No matter what brand of tool you go with, knowing how, when and why to use the tool is the most important.
I agree w/ Handicap. I just bought a D80 last year w/ kit lens and 70-300VR lens. Next thing you know, I got the SB800 flash. Before you know it, I bought the Sigma 10-20mm. Now I'm looking at the type of 2.8 lens he described in his post.

I should have just got the 2.8 in the first place, but being a total noob, I thought I should just get the kit lenses to start with until I figured out what I needed.
DSLRs have a pretty big learning curve if you've never used them before. I have a film SLR, but it's different than the DSLR. I never had to figure out things like ISO settings, etc. If I knew I was taking lower light photos I would buy 400 speed film, or 800 speed film. I didn't really know what I was doing, but it was more WYSIWYG. If it looked blurry, I would refocus until it looked good. My experience w/ my DSLR is that it's different than the older SLRs in this regard. Many times in my DSLR viewfinder the shot looks fine. Then you snap the picture and it's blurry or worse. (Well that's how it was in the begining. It's getting better now.) DSLRS tend to blow out highlights way more than SLRs. So now I'm thinking of picking up a couple of filters to help with that, especially because I love taking pictures of the sky and sunsets, etc. Sometimes, it's impossible to get it so everything is even and nothing is blown out when you are shooting a bright sunset over dark water for example.

(For me anyway, maybe it's becase I'm still learning?

) The point is, I now suffer from Nikon Aquistion Syndrome, LOL! I thought my initial purchase would only be the cost of the camera, kit lens and zoom, couple of extra SD cards, extra battery, bigger camera bag, maybe an external flash for a total of less than $2000. HA! That's what I got for thinking! I have a son who is in marching band (long distance nightime shots w/ fast movements), symphonic band (low light, indoors, no flash allowed), I take a lot of show and concert/dance photos (low light/ no flash), so I needed a fast lens for that. (Got the 50mm f1.8 best/cheapest investment to date! $100!)
So, Handicap is right, it adds up quickly, and you will need a wide variety of lenses to get everything you want because the DSLR is not as intutive as the P&S. Either that or you will have to bump up your ISO for extremely low light photos, in which case you may as well use your P&S. (Unless you already know how to use Photoshop, Lightroom and/or Nikon Capture NX.) If you get the kit lens, you will probably need a tripod to stabilize the camera for any low light shots w/ no flash situations, because the lens isn't fast enough for indoor dancing/recital type photos, especially if you are at a distance. You can't bump up the ISO enough w/out sacrificing quality. (Oh yeah that's right, I also bought a couple of CF tripods, one for home use and a lighter one for lugging around the parks.) Okay, some will tell you to use Noise reduction software, but if you are just starting out in the digital world, for me anyway, I would rather learn to use the camera correctly first and try to learn to get the shot right. Then I can worry about the photo enhancement stuff later. When I can afford it...

After I get my f2.8 lenses -- LOL!
In many ways, the P&S is so much easier to use, especially if it has built in IS. But if you're willing to invest the time into learning how to use the camera, and take a ton of photos and analyze them to try to figure out what you're doing wrong, you can start to take better photos. If I could afford it I would take the NYIP class, just because I am really loving my new hobby, and I am impatient to get better at it. (BTW, my husband loves the pictures, but hates the hobby due to the time and $$$.)
But with all that said, I love

my Nikon D80, I love

the creative experience of figuring out how to get the picture 'right'. Of course, I hate it when it doesn't come out,

especially if it's a once in a lifetime shot. But that's my fault, and that's part of the learning experience. One great thing with Digital is you can take as many as you want with no cost until you develop.
The people on these boards are so helpful, I've learned so much from many of them!

Thanks to all of your pros out there!
Good luck whatever you decide!