Madame de Vionnet is probably the most charming and cultured woman Strether has ever met. Beyond that, he feels totally in awe of her because she is the one who is responsible for Chad's amazing transformation into a European gentleman. He is quick to tell Chad after meeting her, "'You owe her everything—very much more than she can ever owe you. You've in other words duties to her, of the most positive sort; and I don't see what other duties—as the other are presented to you—can be held to go before them'" (12.4.34). That's serious stuff, man.
Madame de Vionnet is therefore not just fine herself, but she spreads fineness into everything she touches. Madame, you see, comes from aristocratic stock, meaning that she has lived her entire life in luxury. She's a Countess, for crying out loud. But instead of squandering her luxury like many people, she has used it for purposes of good and has helped people better themselves.
Of her many fine qualities, Madame de Vionnet is a master of words and double meanings. Madame is especially impressive when she absolutely schools Sarah Pocock in verbal boxing. Every time Sarah wants to say something direct, Madame will say something that can be interpreted in more ways than one, which totally paralyzes Sarah into silence.
As Miss Barrace gleefully notes, "[Sarah's] bricked up, she's buried alive!" by Madame's verbal skills (10.1.93). No one seems to enjoy watching Madame do this more than Strether, who has spent pretty much the entire book being totally afraid of Sarah.
But for all of her majesty, Madame de Vionnet is also a very insecure person. She constantly worries about what Strether thinks of her. She especially goes off the rails when Strether finds out about her and Chad having sex, sobbing that she is "old and abject and hideous […] Abject above all. Or old above all. It's when one's old that it's worst" (12.2.20). Whoa. Melodramatic, much?
Basically, she knows that she has deceived Strether and has used him as a pawn for keeping Chad in Paris. And in this sense, she's really not any better than Mrs. Newsome. It's this betrayal, actually, that leads to Strether's decision to return to America, and Madame will never forgive herself for it.