I am currently running Simulations in Veins and/or Artery.
Is there an easy way (thats perhaps I just didn't find because I'm blind/stupid) to dump the Output created in the Console into a file, apart from running it slower than express mode and then using copy/paste?
Can I create these data while still running in express-mode?
The short answer: if by 'console output' you mean the event log, then yes you can, but no you shouldn't, for exactly the reason you mention: express mode disables this output. The recommended way to collect data from your simulation is by recording it using "statistics", see also this page of the OMNeT++ tutorial.
You can log this information using the record-eventlog=true option in your omnetpp.ini (as described in more detail in the manual), but this produces huge files for veins and artery. This is because the event log is used more as a logging system. The best way to think of it is as debug output and development support: to quickly figure out why something isn't working correctly. I tried to (ab)use this feature for logging data -- please, save yourself the immense pains and use the statistics module.