Wildlife Photography is more often than not about reach, Therefore the 70-300 has the advantage, however as has been said the 70-200L wins on IQ, build quality etc.
Another option not being considered and would require a little more saving is the 100-400 L....
However if that is not an option, personally, I would go 70-200L f4 IS USM, with a 1.4x converter in my bag. The IS can be invaluable on days when our weather is not brilliant as you get 2 extra stops (slower shutter speed without blur). If you can not stretch to the 70-200 IS, then seriously consider the 70-300 IS...
I would see if you can try both for yourself before you part with your hard earned.....