Any video player will output the same video file the same way
It is not quite true. Well, it is not the video player that makes differences but the codec. E.g., VLC uses their own x264 library to decode H264 videos and https://en.wikipedia.org/wiki/X264#Capabilities tells:
x264 contains some psychovisual enhancements which aim to increase the subjective video quality of the encoded video.
Adaptive quantisation in two modes using VAQ. The second mode, a later addition, adapts the strength per frame in an attempt to improve the quality. Psychovisual Rate–distortion optimization which attempts to maintain a similar complexity. The complexity is measured using a combination of SSD and SATD. Macroblock-tree rate control which controls the quality by tracking how often parts of the frame are used for predicting future frames.
x264 is often said to be the best H264 codec.
