after updating from CS3 to CS6 I am missing the export function (file -> export) for several formats. In AE CS3 I could export my video to swf, mov, wave ... without using the render queue. This was quite useful because of the low file size it was easy to send the draft to the customer.
Does AE CS6 not support this feature anymore, or is there any possibility to "activate" this feature?
Those features are simply gone and ever have been since CS5 due to the transition to 64bit and the relevant Quicktime components no longer being available.
You'll get your best low data rate renders to send to clients by using Adobe Media Encoder. Export was always a sloppy way to make a movie file and resulted in very low quality work. I never used it, ever. I even lobied to completely remove the ability to export any kind of deliverable movie from AE without going through fully adjustable compression options.