Ah, so while taking pictures I might have found a solution to the "problem":
GQRX and SDRConsole seem to use different styles of displaying the spectrum:
GQRX has very small steep lines also when zoomed out and also updates very quickly which leads to belive that the SNR lower. I had to trigger the screenshot exactly right to get this SNR, which comes far closer to the one in SDRConsole.
SDRConsole has a smoother and slower change on the spectrum display which makes seeing the peaks easier. There is also some kind of "smoothing" which decreases when zooming which leads to assuming that the Noise floor is lower. When zooming in this "smoothing" disappears.
So all in all it is a matter of zoom level and the difference in displaying style.
Sorry for bothering but maybe someone will have this "issue" to in the future.