The "faster" (wider the aperture) a lens is, the faster you can set your shutter speed to capture the same image.
Let's say you find that to get a "zero"
0 Ev (exposure value) reading on your camera's meter, your settings with your 18-70mm f/3.5-5.6 "kit lens" @ 50mm were:
f/5.6 (widest possible aperture @ 50mm with this lens)
1/5 sec*
ISO-400
* Which basically exceeds the average performance envelope of having SSS correct for shake
Using the TAMRON 17-50mm f/2.8 @ 50mm, your settings could be:
f/2.8
1/15 sec**
ISO-400
** Which is now within the performance capability of SSS.
To be a bit safer and not push the noise issue, you could up your ISO to 800 and get these settings:
f/2.8
1/30 sec.
ISO-800
"SSS" is well within operating limitations, and you have a faster shutter speed to capture your subject. With the kit lens, you would never be able to achieve as nice and controlled an image.
You will also find that as far as sharp focus and image quality, the TAMRON 17-50 runs rings around the "kit" lens