Parseltongue supposedly the language of snakes, and a Parselmouth the one who speaks it. But do snakes in fact have a language? I would argue that a more accurate definition is that the Parselmouth exudes a magic that imbues in localised snakes extra abilities including
- the ability to understand Parseltongue
- extended intellect - possibly a variable amount of extended intellect based on the Parselmouth's level of focus on the snake in question? Cannon allows for different interpretations.1
- The basilisk appears to have very rudimentary levels of sentience, expressing very animalistic desires only.
- The boa constrictor appears to have an understanding of more abstract concepts like being annoyed by visitors, and home.
- the ability to blink - snakes do not have eyelids to do so in nature.
- an understanding not only of verbal language, but of human style body language, the boa constrictor uses a human style head nod.
The two things of note that lead me down this interpretation are
- the fact that the boa constrictor has more than just a language ability, it uses human winks and nods as well in the presence of a Parselmouth.
- the fact that the basilisk appears to express itself much more the way we expect an animal to - raw barely structured emotion.
This corresponds to the way the Parselmouths in question would have formed their expectations: Harry wanted a conversation and so his magic imbued its target with the ability to respond at a level able to converse. Riddle saw the basilisk only as an animal and a servant, never as a someone. Thus the basilisk was in fact less capable.
While I recognise this is a massive amount of speculation, it fits the facts, and preserves the line between sentience and sapience.