As i said, the paradigm i made is not based on actual prices but to show why someone will opt for better graphics in the first place.
But if you would like me to use actual prices then we could have the two systems bellow,
Core i3 2100 + HD6970 2GB or GTX-570
vs
Core i5 2500K + GTX560 1GB (non Ti) or HD6870
Both HD6790 2GB or GTX-570 can still be used for modern games at adequate Image Quality settings and frame rate.
With the GTX-560 1GB you would have to sacrifice Image Quality settings right from the start. And one,two years later you would have to upgrade the GPU because it would really hold you down in a lot of games.
As i have said before,
going one root or the other you sacrifice something and you will need to spend money again to upgrade later on.
As you can see from the graph bellow, the GTX570 is capable of producing more than 30fps at Very High Quality Image settings even in Watch Dogs. You could tinker a little bit with the settings and have very high Image Quality at higher fps.
On the other hand, with the GTX560 you would have to lower image quality substantially in order to even get 30fps.
Some users will be fine with lower image quality, others will not. As i have said, it is all about the individual user, its needs and priorities.
So at the end, unless you spend more from the start, you will have to upgrade something sooner or later. There is not a single route to take when you are budget constrained, it highly depends upon your needs and sacrifices you are willing to take.