You observe the current statistics of the creature
Disguise self is an illusion that only changes your visible looks. Your actual game characteristics do not change. There are not even other characteristics that you could be fooled about.
The Battle Master fighter's Know your Enemy feature (PHB, p. 73) does not state you need to see the true form of the creature, just that you must "spend at least 1 minute observing or interacting with another creature outside combat", which you can, and you will be able to learn about its characteristics.
The description of the Polymorph spell, however, says (emphasis mine):
The target's game statistics, including mental ability scores, are replaced by the statistics of the chosen beast.
As both the terms statistics and characteristics refer to things like ability scores, hit points, AC, we can conclude they mean the same and can be used interchangeably.
The new statistics replace the original creature's statistics. What your character can observe are the characteristics of this creature, not of the original creature.
Know Your Enemy learns about the characteristics of the observed creature.
You can use this as a test in general: Are the game statistics of the creature actually replaced or modified (rather than just their appearance being changed)? Then these are the statistics you learn about.