Canon user asking for Nikkor advice, please

Greetings, all.  A friend who has a Nikon DSLR (DX, I believe, not sure what model but it's a recent one) is going to Africa in July and wants to photograph birds and other wildlife, and I've volunteered to advise her on a decent but not horribly expensive lens.

I've seen 3 Nikkor options:

1.  80-400 AF VR f/4.5-5.6.  Seems too expensive at $1649, especially given its reputation for very slow AF.

2.  70-300 AF VR f/4.5-5.6.  This looks decent for around $550.

3.  55-300 AF-S DX VR f/4.5-5.6.  Wow, only $250 or so!  But Canon's EF-S 55-250 f/4-5.6 IS is terrific for the price, so maybe this one is too.

So, my questions.  Given that the 80-400 likely will bust her budget and has drawbacks, is there much difference in IQ and AF speed and accuracy between the 55-300 and the 70-300?  Which would you recommend? Is there another Nikkor lens I'm overlooking?  Is there anything comparable or better from Sigma or Tamron?  (Judging from my experience with Canon, I'm going to guess not.)

Thanks much.

FF