Distortion's not that big an issue with most lenses now that we have one-click software lens correction profile capability. One issue is future resale value: the Nikon lens will hold its value for a decade or more, the Tamron...not so much. I'd go more by size and weight and hassle factor. 70-200mm f/2.8 lenses are all, universally, big and heavy, and draw a lot of attention wherever they are used. The smaller lens profile and half the wight mean for traveling and day-trips and such, the lighter, smaller lens has the advantage. I feel the same way about the 70-200/2.8 versus Nikon 70-300 VR lens...I've started leaving the 70-200 at home and going with the smaller, lighter lens which also has another 100mm of top-end reach. As with so many things, there are trade-offs.
The older 70-200 VR is plenty sharp--as long as the image is made on a crop-sensor body. The central part of the image is extremely sharp, and it has lovely bokeh, but the edges of the field on FX are simply not up to 24-MP or 36-MP FX sensor standards,even stopped down to f/7.1. The older 70-200VR is a superb lens on a crop-sensor body, and has lighting fast AF, and its skinny,skinny barrel makes it handle absolutely fantastic. (I've owned mine since the week it hit the US market,and it was my favorite lens until I went to 24-MP FX.)