You don't get more resolution if both sensors are 6K, however the lens on the larger format doesn't have to be as high a MTF because you can resolve fewer lines per millimeter if that area of detail is captured with more millimeters compared to the smaller format.
You'd probably notice less depth of field in general because if the format is twice as large, you effectively lose 2-stops of depth of field if you match field of view, distance, and f-stop between the two formats. So the 65mm movie shot on a 50mm at f/2.8 would look like the 35mm movie shot on a 25mm at f/1.4, more or less. Which means in theory you could match the depth of field, particularly since many large format lenses don't go to f/1.4.
You'd have less noise / more sensitivity probably with the larger sensor since the photosites could be larger, if both formats were 6K.
You may notice the optical artifacts of the larger format lenses, they may feel different - some of those lenses are older and have a bit more barrel distortion and fall-off in the corners.