You're going to have to stop down the Tamron to about f/3.5 or f/4 to get better IQ. This is true in general for lenses of its class. OTOH the FA43 is just coming into its own at f/2.8, so it will indeed beat the pants off the Tamron at that aperture.
See if you can get pretty good shots from the Tamron stopped down to those apertures. If not, then it's possible your copy isn't so good. Tamron - in particular - has a reputation for having a higher than average % of poorer copies out there. So much so that there have been rumors that they keep the best copies for sale in Japan, and some people have made a point of buying their Tamron lens(es) while there.
Either way, part of what you're seeing is just the cost you pay for the convenience of having a zoom. If you have to stop down the Tamron two full stops, then it's really not that good. But if around one stop gives you images you like, you may still have a very useful tool there.
Although I don't live and die by MTF charts, they can do a fairly good job of guiding you as to where the sweet spots are for a lens. As you can see from these charts, a good copy of the Tamron will yield nice results somewhere
between f/2.8 and f/4. Exactly where the better IQ starts is up to you to decide - by taking more test shots with your lens. It could be much improved at f/3.2 - or you may have to go all the way to f/4. Here are the Photozone charts, which make it pretty clear the lens will be weaker at f/2.8:
Tamron AF 28-75mm f/2.8 SP XR Di LD Aspherical (IF) (Nikon) - Review / Lab Test Report - Analysis