First of all, my issue with the Mac Pro looks totally different than the screenshots posted here. It was more of a flickering effect, where parts of the screen have been drawn a second time at the lower part of my ACD 23" and reappeared for a split second, as soon as I did something with my mouse. It was not steady, but started when you used the computer. Therefore it looks indeed like a graphic card issue.
Second, I did something since I posted my issue above and it seems to have fixed it so far. I wanted to wait a little to be sure about that. I switched the display port connectors around. Before my NEC PA241W was hooked up in port 1 using a display port adapter and my ACD 23" was in the port 2 with the normal ACD connector. I switched both around, just to see if the effect would come up on the PA241W as well. It didn't.
So far so good but strange anyway. Something clearly must be wrong with certain graphic card setups in Mavericks, no doubt about that. My machine was running silky smooth for years with several OS X versions.