Based on my own person experience, I am much happier with a digital SLR than a point-and-shoot. With the SLR (you can change lenses and manually focus by turning the lens) I can easily control focus, which is critical for tight close-ups.
I found the p&s to be frustrating when I wanted to get the eyes in focus for a close-up.
Also, the SLR I have (Nikon d70) has much better autofocus than the digital P&S's I had (nikon 5400 and Olympus C3030). If you are going to photograph moving kids or animals, and you need the camera to help you follow the action, then an SLR may be the best option.
Of course, the P&S cameras from Nikon come with great macro functions. The lens that comes packaged with the d70 (the 18-70) doesn't focus very closely. It's a great lens for kid photos and larger animals, but I ended up buying a $400 Sigma macro lens for real close-ups. On the other hand, the P&S close-ups require you to get within an inch or so for maximum magnification, while the Macro lens on the SLR positions you within a foot of the subject.
So, from my experience, the SLR is better for action photography and subjects that require easily adjusted critical focus. If the subjects you'll be shooting are more static and you have time to work on the focus, then a P&S is the way to go. Also the P&S has much cheaper options.
As for brands, I'm not sure I would push the Nikon P&S cameras. I found the focus to be really bad in low light situations. The Olympus was better at autofocus, but didn't have macro function. With an SLR, if the autofocus won't work, you just switch it off and manually focus the lens.
I'll post a couple photos - one from the d70/sigma macro (tight close-up on frog) and one from the Nikon 5400 (frog under red heat lamp).

