I wrote most of my information at both sites, but here is a summary.
My tests showed some things: When you are using Catalyst and VSync is - in any kind - involved, the game will become extremely sluggish and slow. You will feel like you're drunk - I think you call it input lag. With it come low FPS and short intervals of almost smooth gameplay and horribly low-fps lags).
If you deactivate VSync, it runs much better, but you have extreme Tearing. Additionally, in both cases, the performance is low and jumping through portals or creating them for the first time in a level causes a short fixed-image.
Even though I have an AMD HD 7950 Boost, which should do both games fine, it is mostly unplayable.
Portal 2 is better in general, but still not really satisfying.
Then I tried the open source radeonSi drivers. I was surprised to see how good they run. There are some low FPS scenes (mostly in Portal 2, when you have both portals in your field of vision, and using lasers and so on..), but the input lag is completely gone and it is much smoother and with better performance. I played both games to the end with radeonsi and it was fine. This concurs with my research, where I found a lot of posts about this problems being AMD specific and not affecting nvidia. Now it seems like it is driver-specific to Catalyst.
Steam offers a free Portal Demo on Portal's store page, if it helps reproducing.
So, does anyone have an idea about why this is happening and how it can be fixed?