Based on your requirements, either camera will fit the bill rather nicely. The Nikon has a richer feature set, but then you're paying more money for it. Canon and Nikon cameras don't line up together, they stagger and that's reflected in the price points. The XT is better than the D40, the D50 is arguably better thahn the XT the XTi is arguably better than the D50, the D80 is arguably better than the XTi, the 30D is arguably better than the D80, etc. And that's how the prices line up as well - it isn't an accident.
There is nothing in your list of requirements that says you NEED the added features of the D80. Only you can answer whether you WANT them or not. For your stated purposes, you'll get comparable results with both cameras. If you haven't already done so, handle both cameras yourself and simply go with the one that feels best to you.
Also, let me highlight - for your stated use for indoors - you really do want an external flash. To me that is infinitely more useful than spending your money on 2.8 lenses which still won't be fast enough for your indoor shots. Get a good flash and you can be shooting at f8 without problems.
As for a lens, in Canon system I would suggest 17-85mm and in Nikon the 18-135. Again, I don't see how spending money on a 2.8 lens will be of great benefit - kids moving around indoors - you'll get better results with the flash then you would with 2.8 (which would force you to shoot at high ISO and the kids would still have to stay still unless you have a VERY brightly lit house). Spend the money on the flash, not wide aperture lense, IMO.
So, my recommendations:
Canon XTi with 17-85mm lens and 430ex flash
Nikon D80 with 18-135 and SB-600 flash
Pick the camera that feels best to you. The good news is: you can't make a bad decision.