A flesh golem is like the Frankenstein monster. A flesh golem is based on the monster. In the end though it is not the monster. There are two distinct reasons for this.
The first reason is that the Frankenstein monster is not taking commands. It has free will and enough intelligences to use said free will. A golem in D&D terms is a construct. It even lacks an intelligences score so is incapable of the thought needed for self awareness. If a flesh golem goes on a rampage it is either because it was told to do so or its programming got messed up. It kills a little girl and does not care. The Frankenstein monster sure cared and emoted about it. The monster can even speak if you go by the actually story and not the lame movie. That's right, the monster can speak and in fact was eloquent, educated, and well-mannered. Now all people think of the monster is that he grunts, a serious loss of ability compared to being able to fluently speak french.
The second reason is that a flesh golem is not alive. It is a shell for magical energy to move like a puppet. The Frankenstein monster is alive, not a construct, and definitely not undead. Sure he was made up of a number of different peoples part's but that changes nothing. If it did that would mean someone who had a heart transplant is in fact a flesh golem. After all by definition not having a heart would mean death and the transplant heart was definitely dead so putting the two together and making a living being would be about the same. Even if you argue the percentage of the original person still there what happens if the same person also had to get a number of other transplants? Is there a point when you become a flesh golem or something, maybe it's at 51% no longer being original that it happens. "Opps sorry miss, that kidney transplant pushed you over the limit, your a golem now." and then the audience laughs.
The Frankenstein monster is a thousand times better then a flesh golem. Seriously, who would make flesh golem anyway? Silly necromancer wannabee, your undead minion is in another castle but here have a free golem.