As has been well covered in the question What does "viewfinder magnification" mean?, the magnification rating number of any viewfinder is based on a specific focal length lens. If you double the focal length of the lens from 50mm to 100mm, you also double the amount of magnification the viewfinder provides compared to looking at the world with just your eye.
Of the two cameras you are comparing, one is a Full Frame body with a 24mm X 36mm sensor, and the other is a crop sensor body with a 15.8mm X 23.6mm APS-C sensor. Since magnification numbers are based on a specific lens at a specific aperture focused to infinity, if both manufacturers do not use identical lenses (hardly likely since they do not share the same mount), the magnification numbers provided by the manufacturers can not be directly compared since differences in the characteristics of the lenses used will affect the calculated magnification number.
If you look at the Nikon D300 review at DPReview, you will see that with a 50mm f/1.4 lens the D300 was measured at approximately 0.94x. The Canon 6D review at DPReview lists the 6D viewfinder magnification as 0.71x but does not include the lens information used to obtain that number. 50mm is generally the standard used.
What you must realize when comparing the viewfinder magnification of these two cameras is that the same focal length lens on each will NOT provide the same angle of view since their sensor sizes are markedly different! In the case of the APS-C sized sensor in the Nikon D300, you must use a lens of approximately 33mm to provide the same field of view (FoV) in a picture as the use of a 50mm lens on the full frame sensor of the Canon 6D. Since the arithmetic here is linear, to calculate the magnification factor of the D300 viewfinder with a 33mm lens you would divide 33mm by 50mm. 33/50 X 0.94x = 0.6204x. What this reveals is that when both cameras have lenses mounted that provide the same FoV, the 0.71x image in the 6D viewfinder is larger than the 0.62x image in the D300 viewfinder. Even when taking the viewfinder coverage into account (6D=97%, D300=100%) the image in the 6D viewfinder will still appear to be about 11% larger in linear terms and 24% larger in terms of area when viewed from the same distance behind the viewfinder.
The D300 viewfinder appears to the viewer whose eye is at the specified eye relief distance to be 100% of .94x the linear size of a 15.8mm X 23.6mm sensor. (15.8mm/23.6mm*0.94*100%=14.852mm tall/22.184mm wide).
The 6D viewfinder appears to the viewer whose eye is at the specified eye relief distance to be 97% of .71x the size of a 24mm X 36mm sensor (24mm/36mm*0.71*97%=16.5288mm tall/24.7932mm wide).
The total area of the D300 viewfinder will appear to be 329.476768mm².
The total area of the 6D viewfinder will appear to be 409.80184416mm².
That's about 24% more area which is the same relative size of a 22.5" monitor compared to a 20" monitor!
Because the coverage of a lens on a FF camera covers a much wider angle of view than the same lens on a crop sensor camera, the magnification of the FF camera must be less in order to show the wider angle of view provided by that lens on a FF camera than the magnification in a viewfinder of a crop sensor camera that only shows the reduced angle of view that same lens provides to the cropped sensor. Since light magnified more is also spread out further, the crop sensor viewfinder (D300) will be noticeably dimmer (about 79% as bright) than the FF viewfinder (6D).
Also, The 6D is superior to the D300 in almost every way where it matters most: Image Quality. If your primary concern is what things look like through the viewfinder, there are plenty of used film cameras available for a pittance that will outperform almost any DSLR on the market.
From a comment to another answer:
It's hard to trust those numbers as they seem to include the coverage, and as it's said "Magnification is a relative measure which compares the size of what we see through the viewfinder to what we would be seeing without looking through a viewfinder". So whatever the coverage is 100% or 10%, it's not because you only see a small percentage of something that the said something size is different. Same thing for the crop factor : take a little window, and zoom whatever is displayed into that window, the size of the window will remain the same. And what I want to find is that Window's size.
The size of the window is the size of the sensor of each camera multiplied by the viewfinder's coverage. If you "...zoom whatever is displayed in that window..." you have changed the magnification factor provided by the lens!
That is why a crop sensor makes the subject look larger than a FF camera when both images use the same focal length shot from the same distance and are displayed at the same size: because the picture from the smaller sensor has to be magnified more to make it the same display size as the picture captured by the larger sensor. Crop sensors don't "zoom" a lens. They don't make the virtual image projected by the lens any larger. They just collect less of what the lens is projecting. Then to display that smaller portion captured by the smaller sensor at the same display size as the larger portion captured by the larger sensor the display magnification for the picture taken with the smaller sensor is increased by the sensor's crop factor. Here's the key to understanding viewfinder magnification: display magnification is done to the picture after the sensor captures a portion of the virtual image projected by the lens and takes a picture. Viewfinder magnification is based on what the lens does to the light before it strikes the sensor.
Look at it this way: If we take a photo of a penny that is 19mm in diameter with a 1:1 macro lens the size of the penny is the same in the virtual image projected by the lens no matter what the sensor size is. The projected image of the penny will be too large for all of it to fit on the 23.6x15.8mm sensor of the Nikon D300. The projected image of the penny will fit easily in the center of the 36x24mm sensor of the 6D and there will be room to spare. The penny is only 19mm across and the sensor is 24mm tall and 36mm wide.
Now, imagine both cameras have viewfinders with the same magnification. That means the size of the details of the penny will be the same in both viewfinders. If the viewfinder of the crop sensor camera has 100% coverage, it is only going to show the parts of the penny that are projected onto the smaller sensor. If the viewfinder of the FF camera has 97% coverage, it's still going to be large enough to show the entire penny. The missing 3% will be from the edges of the image projected onto the larger sensor that are outside the edges of the penny. That means the "window" for the APS-C camera is smaller if it can only see part of the penny that is magnified at the same size in both viewfinders. The window for the FF camera is larger since it is big enough to show the penny and some of the surrounding area. The size of the details of the penny will be the same in both viewfinders, but the larger viewfinder will allow one to see more of the penny.