It's OK to start a new thread!
You probably wouldn't notice much difference in sharpness just displaying the images on a typical monitor and viewing at a normal distance. However the EF17-55 is f2.8 across the whole focal length range, with the 16-300 the maximum aperture varies from f3.5 at 16mm to f5 at 55mm, so it's 2/3 to 1 2/3 stops slower, so there's that to consider. The Tamron 70-300 VC is a very good lens and covers full frame should you ever go that route.
However purely in terms of convenience, the Tamron 16-300 is obviously the winner