... What I want to know is at the exactly identical conditions (iso, shutter speed and aperture) what exactly will be difference in the picture captured.
Which differences will be noticeable and which ones won't can be highly dependent upon the particular ISO, shutter speed, or aperture selected. What may not be noticeable when the lens is used at f/8 on both cameras may well be noticeable when f/1.8 (differences in DoF) or f/22 (differences in diffraction) are used. What may not be very noticeable for images taken with each camera in very bright light at ISO 100 will be much more noticeable for images taken with each camera in a low light environment at ISO 3200. The difference between the magnification needed to display images from each camera at the same size may not show much of a difference in camera motion blur with fast shutter times above 1/1000 second or so but may be more apparent at slower shutter times of around 1/30 second.
The most noticeable difference will be the wider field of view provided by using the same lens with a larger sensor. Please understand that the focal length and magnification power of the lens doesn't change. What does change is how much of the virtual image projected by the lens is captured by the larger sensor. If images from your APS-C camera and a FF camera are viewed at the same size, the image from the 1200D must be magnified by a factor of 1.6X more than the image from a 5D Mark II.
If you want to shoot the same subjects at the same size in the frame, you will need to get closer to the subject to get roughly the same framing. This will affect things such as perspective, which is determined by shooting distance. Changing the ratio between the distance to the subject and the distance to the background will also affect things such as how much the background is blurred and the apparent relative sizes between your subject and background.
If you want to shoot the same subjects at the same distance, the perspective will be the same but the apparent size of the subject will be smaller by a factor of 1.6X.
Because of the FoV differences the larger sensor uses light from closer to the edge of the image circle projected by the lens than the smaller sensor does. With most lenses, including the various 50mm f/1.8 iterations from Canon, optical quality is best in the center of the image circle and any aberrations are most noticeable at the edges. The difference is most noticeable when using larger apertures. This is somewhat ameliorated by the lower magnification needed to view the FF images at the same size as images from an APS-C camera. In the center of the frame, a FF camera should produce a sharper image than an APS-C camera using the same lens when images from both are viewed at the same size. But on the edges the IQ will probably be a little less from the FF camera compared to the APS-C camera. This is particularly true of wider angle and normal lenses. By the telephoto range aberrations that affect the IQ at the edge of the image circle are much easier to correct than with lenses that have a wider field of view.
Your EOS 1200D has 18MP that are each 4.3µm wide. The 5D Mark II has 21MP that are each 6.4µm wide. With the 5D Mark II you not only get more pixels, which can increase the resolution of your images if the resolution limits of the lens isn't a more limiting factor, but those larger pixels mean greater dynamic range when comparing sensors from the same basic design and generation of technology. Larger pixels can absorb more light before they reach full well capacity than smaller ones can. This increase in dynamic range allows for capturing the same scene with a higher signal to noise ratio (SNR or S/N ratio). This will be particularly noticeable when shooting in low light. Although your EOS Rebel T5/1200D was introduced in 2014 compared to the EOS 5D Mark II introduced six years earlier in 2008, the 1200D uses much of the same technology as the 5D Mark II. The 18mp sensor used in the EOS 1200D is essentially the same sensor introduced with the EOS 7D in 2009. The DiG!C 5 processor used in the 1200D is the same DiG!C 5 processor used in the 5D Mark II. Canon tends to "trickle down" technology used in their top tier products when it was cutting edge to their lower end products when that same technology is a generation or two older. So even though it is a 5-6 years newer design than the EOS 5D Mark II, the EOS 1200D uses essentially the same generation of technology in the sensor and image processor.
The AF systems in the two cameras are very similar, but the 5D Mark II gives you the ability to do Auto Focus Micro Adjustment to correct for slight front or back focusing issues. Sometimes what appears to be a soft lens is really just a lens and body that need to be calibrated to each other. The 1200D requires the camera and lens take a trip together to a factory service center to do the same thing.
The larger pixels of the FF 5D Mark II also allow the use of narrower apertures before the effects of diffraction become noticeable. For a fuller explanation of diffraction please see this answer to Do smaller apertures provide more depth of field past the diffraction limit, even if peak sharpness suffers?