ok let's see:
laptop:
A: Atheros AR5B93
B: No special tool used
C: In the router admin pages, I go to status then click wireless, there I see for every wireless client:
mac address, ip address, mode, rate, signal.
the mode is 11ng
The laptop reports 100 percent signal, the xbox 94-98 percent
the laptop rate is either 54 or 108 it seems. the xbox either 1 or 5.5
360:
A: Yes, the slim with built-in wireless N.
B: slim
C: same as laptop. They are both on the ground floor. The modem/router location makes it physically impracticle to use wires, but the distance is rather short with only two thin walls in between.
The laptop and 360 are about 5 meter apart.
General:
Here comes the shame on me part. It worked fine at first, so I never really bothered checking the status screen, no idea what the rate was back then. Then after two weeks microsoft publishes by accident a faulty update on november 1. xbox live actually was down but it reported that my MTU was too low. Then I started googling and changing around settings to what other people reported worked for them. However, since the problem was in xbox live, not my mtu, there's no way this would work. Had MS communicated this clearly I wouldn't have spent half a night trying to correct things. Now when I set things back to what I think they were, and setting things back to your recommendation, it still doesn't work, though by now the xbox live service is fully functioning again...
It's actually getting worse by now. Most of the time I can't connect at all. the 360 gets a local ip address starting with 169 instead of the normal 192 range. Only occasionally after testing the connection a couple of times does it even connect. And when it does get a 192 range ip, it reports that mtu is too low, should be at least 1365. My router is configured at 1500. I tried lowering towards 1365 but that doesn't help either.
Hope I made some sense there. Though I'm not computer illiterate, I'm also not a networking engineer and a lot of this is difficult to grasp. I wish I could adopt a more consumer approach, you know, connect cable, push button, enjoy....