Part of the answer depends on whether or not shooting in 4K is important to you and that is something only you can decide. Are manual controls important to you?
Canon G40 probably has better low-light performance than the Sony.
Not that this is a deal breaker but the Canon has a slightly larger touch screen than the Sony (3.5" vs 3").
According to the reviews of the Sony FDR-AX53/B one drawback is that you are only allowed to change one manual setting at a time. This means if you adjust the aperture the other adjustments are made for you based on the aperture setting you choose. Another known issue for the Sony camcorder is camera shake/stuttering when placed on a tripod. This issue is not reported when shooting handheld. I'm...