Which of these cameras is a better deal?
Nikon D3100 with Nikon AF-S NIKKOR 18-55mm 1:3.5-5.6G Lens, wireless remote, ens Pen, Lens Cloth, Jet Blower, and Nikon Camera Bag, Amazon Basics Sling Camera Bag for $300
or
Canon Rebel t3i with 18-55mm lens, 75-300mm lens, 2x HD telephoto MC lens, 45x wide angle MC lens, HD filter kit, UV filter, Digital card reader/writer for $475
The accessories listed should be avoided. The cameras are being packaged with these cheap accessories to increase the profit margin of the kit. You can get much better accessories by choosing them yourself.
In all honesty, the kit 18-55 lenses are considered to be the worst lenses made by either Canon or Nikon - actually they're not even made by Canon or Nikon, but rather contracted out to places like China to lower the cost of the lens. You'd be better off just getting the body and a lens by Canon/Nikon or by Sigma, Tamron for just a bit more.
Screw-in adapters are junk, don't bother with any package that includes them - the Canon 75-300mm is also a bit of a dog.
If you want a DSLR, get body and 18-55mm with a couple of SD cards to start with.
Find a dealer, look at All the alternatives (you have to be Really stupid to only look at Canon and Nikon, when Pentax have advantages over both, and Sony shoot better video), HANDLE a couple, and choose the one that feels best in your hands.
Having just had a quick trawl through Amazon, $300 seems too good to be true. The body alone is just under $300 and many places don't sell it any more because it's quite an old camera now. The likelihood is that the 18-55 lens with both the Nikon and Canon is the older version, so offers like this with the additional accessories are just an excuse to clear shelf space of old stock.
Both are consumer cameras and both do much the same thing and will give you much the same photos. Some people like Nikon, some like Canon. There's also Pentax and Sony.
Long term you may want additional lenses or other equipment and that's where things get expensive. You will need additional SD cards, perhaps a spare battery, a tripod, an external flash. Buying the camera is just the start.
Don't just rely on Amazon, there are other sellers. Looking around you can get the Nikon 3200 with a few bits and pieces for $476 and the 3200 is probably better than the T3i, though, again, they are both consumer cameras and will take much the same photos.
Nikon D3100 is best your.go for it.