Differences between women and men.

[DLJ]

...
 but maybe there is a difference in the way it feels to be in the world soaked in estrogen vs in a testosterone modified body/brain?  My hunch is that there might be a difference in the way it feels to be male vs female, but how would we ever know?

There are aspects that can be experienced.

Bio-chemistry: Take the hormones (if you're feeling brave).

Environment: You could do a Tootsie (there are a few YouTube vids of both men and women trying this experiment).

Virtual Environment: You could set up an on-line dating (or facebook or whatever young kids use nowadays) profile as someone of the opposite sex (or sexual preference).
- I've tried this. I swapped profiles with a young female friend for a while. Afterwards, we compared notes.
She reported (I paraphrase): "OMG! I was just trying to be nice to people and they treated me like I was a creep".
I reported: I hate all men!

Societal conditioning and Bias: Although bias can be experienced in the above experiments, societal conditioning can't be simulated because it starts from the moment you're born... you cannot simultaneously experience what it's like to grow up as male and female (or all five of the Indonesian model)... unless reincarnation is a thing.

To Excited Penguin: I note your point regarding "environment" vs. "social" but respectfully side with Irrational.
I prefer:
Biological/environmental
Genetic/memetic
Individual/collective (organisational)
Personal/societal
... but I'm unlikely to be consistent on this.