I cannot speak to the Canon offerings - they, unfortunately, never "felt right" in my hands. I have a Nikon D90, and have been using the 70-300VR for birding, for the last year, or so... Regardless of your decision, be sure to test any camera/lens you're thinking of buying and, if at all possible, bring a laptop with you, to really see what the outputs are like... Also, pay close attention to the view finder - they are not all created equal, and you will find certain cameras have a FAR better one to assess focus, etc...
The Nikon D3000 is an entry-level DSLR, but don't let the term fool you. The 10.2MP sensor tags up with an 11-point auto focus system (like my D90), which is okay for tracking moving subjects (like birds in flight), but you'll have to work to get good shots, and expect to lose some out of focus. At 3 frames per second, though, the D3000 does only a decent job at capturing speedy subjects; faster would be better for flying birds.
Smaller size + lower cost means some compromises, when it comes to a DSLR. The sensor is a few years old (though used in higher-end cameras back them); the 230,000 dot 3.0 inch LCD is okay; and the ability to manually control all options is quite limited. This truly is a beginner’s camera, in many respects. But, at it's price, there is good bang-for-the-buck, and perhaps the shortcomings are negated by cost. If you can swing it, the D5000/D90/D300/D300s all handle high ISO better than the D3000 (better pictures in less than perfect lighting). They all cost more, but also offer more "birding friendly" features, like faster frames/second (and the D300/D300s have a MUCH better autofocus system). I found the D90 to be a nice balance of price and performance...
The 70-300VR is a very good CONSUMER lens, particularly for the price. Sharper than most, and VR works very well. The slower aperature will limit you in low light and there are some other compromises, such as some softness and the autfocus speed. The lens is quite sharp in the 70-200 range, even wide open, but 200-250 takes a little hit, and beyond 250mm the lens is best stopped down. Problem is, if you're shooting birds, you'll likely be @300mm ALL THE TIME, and still wanting for longer reach. The lens will be best in good light, but one of the better bodies would allow you to use a higher ISO in darker conditions, too...
Eventually, most come to the conclusion that a dedicated birding lens will be required... I got there a while ago and starting saving... Just this week, I picked up a Nikon 300mm f4 AF-S and a 1.7 teleconverter (stretching it out to 500mm f6.7). I haven't had a chance to do any substancial testing, but can clearly see the difference is sharpness @ 300mm, and even with the 1.7tc on, @500mm. This is the best birding option for those on a budget, as the faster/bigger glass is A LOT pricier...
The 70-300VR is still in my kit, and will not be discarded. For a trip to the zoo / larger wildlife, and general use, it's a perfect option. For birding, the 300mm will be the lens of choice. Here are a couple of 70-300VR samples (i have none from the 300f4, yet):
