Some of those games have a tendency to stream textures from the hard drive rather than keep them resident in video memory. This is a symptom of a game being developed for both PC and console. The Assassin's Creed games even slow down on my computer but Skyrim is usually pretty good.
One solution to deal with games that stream data is to install them to an SSD
The 560ti 448 is no wimpy card and should be on par with the 6950 at least. If it seems like you should be getting better performance than you are then you might want to try a few tweaks such as turning VSync off and/or limiting the framerate to the refresh rate of your monitor (usually 60fps). Some game engines do not respond well to sharp changes in the framerate.
There's not much you can do about Assassin's Creed, the game isn't optimized at all. Skyrim shouldn't give you many troubles though
A GTX 670 is going to perform better than a GeForce 6700 when paired with the same Pentium 4 processor and a 16x PCIe 1.x bus. Any gameplay will be limited purely by the fact that the Pentium 4 processors were horrible for gaming