Regarding IQ, the 70-200 f/2.8L II IS is best, the 70-200 f/4L IS is 2nd best, and then the 70-200 f/2.8L I lens. It is a very good lens.
I had the non-IS, OK
had the IS v1, OK at the short end and very soft at the long end.*
sold it, got the v2, very nice and sharp, some CA in FF corners.
Found v2 could render some absolutely hideous bokeh at times, too often for my liking, so sold it too. Busy backgrounds that were near the transition zone could look aweful, not like the smoother rendering of other lenses. That can be the price you pay for a well-corrected lens.
I prefer the overall image balance I get from am older Tamron, pre VC model. The newest Tamron is pretty decent for the $ if you don't need the toughness or caché of the big white piece of pipe. What you save there allows you to buy their 24-70/2.8 VC also.
It really depends on what you need the lens to do. There's more to consider than just sharpness or how effective the stabilization is or how much CA there is.
* Turned out my v1 was not so much soft at the long end as front focusing quite badly at greater subject distances. Discovered that when MF'd images at 200mm were considerably sharper than AF shots.