Short answer: Yes, No and Yes.
"Do these aspects cover all the bases that Str, Con, Dex....etc do?"
I am answering this question as if it were "Do these attributes cover all the attributes that Dungeons and Dragons includes?"
They do, if you replace what the character prefers to do with what they can do. Using the sample attributes you have posted here, someone with high Charm would prefer to convince people to share his/hers point of view and/or distract them from the real point of a conversation. In Dungeons and Dragons however, someone with low Charisma is incapable of (or really rather bad at) convincing or verbally manipulating another. In the system you have posted it is clear that a character with high Charm prefers manipulating people, but it is unclear whether they are capable of (and how effective they are at) verbal manipulation. (I am assuming you originally wanted the system to represent skill over preference, and just worded your question in a different/wrong way, as preference is completely binary, while skill has a curve.)
The same goes for other attributes as well, I just used Charm as an example.
"Do they cover the bases that the WoD statline covers?"
I feel the only attributes in oWoD that are not reflected by yours are Appearance and Endurance. In your system, Charm and Heart reflect preferences on social approaching, while Appearance is, well, how beautiful your character is. Don't worry though, I always thought that Appearance was the most stupid attribute in the history of pen and paper RPG's ever, so don't include anything similar, I'd say.
Also, someone with high Brute seems to prefer direct, brute force approaches that might resolve a situation quicker, and that someone with high Finesse prefers a slow, but more delicate and careful resolution, but there is no attribute to reflect how long a character can keep trying to do physically taxing tasks (running, jumping, climbing, etc.)
Apart from these two oWoD attributes, I'd say all the rest are reflected well.
"Is a character with these as stats missing some functionality I can't think of?"
Apart from oWoD Endurance/ D&D Constitution, You have covered the majority of the ground that most popular pen and paper RPG's cover, as far as attributes go. However, as humans are very complex beings, there will always be aspects of the human mind, more so than the body, that play a vital role in social interaction and mental challenges and that will elude most people, or that are being passed off as too trivial by others. Examples include, but are not limited to:
Expression: Does Sam know what gestures to use when conversing to further his point? Can he control his microexpressions consciously while conversing? How good is he at using body language to get a point across?
High Expression: Sam knows that when Lord Downey asks him if he has any children, he should not blink when he says "no", otherwise Lord Downey might know he is lying and seek leverage by endagering his son.
Low Expression: Sam thinks that shaking his head vividly left and right when he says "no" in reply to Lord Downey asking him if he has children, will convince him that he hasn't.
Empathy: How good is Sam at noticing people's stances and gestures or microexpressions while conversing? How good is he at 'reading between the lines', meaning, how good is he at examining what people say and how they say it, to be able to uncover what they are truly thinking and feeling by what words they choose and how they say them?
High Empathy: Sam knows that Lord Downey is feeling righteous about trying to frame him with the packet of arsenic because the Lord answers with questions that try to make Sam admit he has often acted with the belief that his opinions are over the laws of the city.
Low Empathy: Sam isn't sure whether Lord Downey is feeling remorseful or righteous.
Critical Thought: How good is Sam at judging how he should deal with a situation to provide him with the result he will be most satisfied with?
High C.T.: Sam knows he will get more answers out of Lord Downey if he respects him as an enemy and if he threatens his position of power within the Assassins Guild.
Low C.T.: Sam thinks trying to appeal to Lord Downey's morals will bring out the good in him, making him confess.
Captain Sir Samuel Vimes Lord Downey
Notes to consider/Afterthoughts/Suggestions:
Make your attributes represent competence, more than preference.
Think about how much detail you want your system attributes to go into, before deciding what to include (example, does Charm include how good a character is at getting his point across and how good he is at sensing what the other people's motives and feelings are, or do you want the two to be separate attributes?)
Discern between knowledge , education and intelligence; The three are completely different. Knowledge is gained through education, but also from experience and perception. Intelligence is inherent from the minute someone is born, and cannot change through natural means. Perception is altogether different, but can be raised through training.
Good luck with your system and feel free to ask any other questions you may have! Have fun!
I would suggest the excellent Dungeon World where you gain new moves when you level up instead of getting numeric increases to your stats.
It keeps the flavor of the D&D worlds while taking a whole new perspective on roleplaying.
That perspective was actually introduced in Apocalypse World, which spawned a series of *World games