You expected it to be better because people tend to think, bigger = better. People talk about how great full frame is without understanding what is really different, and your expectations are too great.
Sensitivity and Noise
Full-frame sensors have larger sensels than crop sensors that produce the same number of megapixels. For sensors of the same generation, full-frame sensors are expected to have an advantage in ISO sensitivity and noise. However:
The advantage is reduced on full-frame sensors that use smaller sensels to produce more megapixels.
The advantage applies primarily to high-ISO. Noise is minimized at low-ISO, such as those you used to take your test shots.
Sensible lens choices, with faster apertures, reduce the need to push ISO.
Newer technologies increase light sensitivity and reduce noise. However, Canon tends to develop technologies slower than molasses, and the EOS 5D mk2 was current throughout the 600D life-cycle. (This is why Sony has a 5-year head start on full-frame mirrorless.)
To see the noise difference between crop and full-frame, you need to take multiple ISO-matched images throughout the ISO range. View them at 100% without resizing. You should see noise become unacceptable at lower ISO settings on the crop sensor vs the full frame.
The "Full-Frame" Look
What your test images demonstrate is, when taking photographs from the same position, with the same lens, with the same settings, everything is the same between crop sensor and full frame, except field of view. Changing sensor size just changes the portion of the (exact same) imaging circle that is recorded.
What creates the "full frame look" is what people do to compensate for the different field of view. To fill the frame with the subject on a full-frame sensor, the camera has to be closer or the lens has to have a longer focal length. The difference can be reduced on crop sensors by using faster apertures, when available.