If a member of the aristocracy married a Princess whose title would change, his or hers?

Men do not take titles from women, so the man's title would remain unchanged. It is however customary for the monarch to offer an Earldom to a man who marries a Princess if he has a lower title or no title at all. When a woman marries she takes her husband's title if it is higher than her own, otherwise she keeps her higher title and appends her husband's title after hers. For example, when HRH The Princess Mary married Viscount Lascelles (later the Earl of Harewood) she became HRH The Princess Mary, Viscountess Lascelles. If a Baroness had married the Viscount instead, she would have been known as simply Viscountess Lascelles, since a Viscount is higher than a Baron.

Baron's are addressed as 'My Lord' - their sons do not receive titles but like the younger sons of Earls and all sons of a Viscount, the sons of a Baron are addressed as 'The Honourable Mr. Such and Such'.

The Princess remains a princess, but she adds her husband's titles to her own. A real life example was Princess Margaret; she married the Earl of Snowdon, Viscount Linley,and her titles were Princess Margaret, Countess of Snowdon, Viscountess Linley.

The rule is that women assume titles and stylings of their husbands, but men do not. Men must have their own titles or be bestowed one in their own rights.

Here is a website that explains titles:

http://laura.chinet.com/html/titles01.html

A baron's son does not have a title. He is the Honorable Mr.--- -----.

A baron bears the honorific of Lord. He is addressed as Lord Surname, followed by My Lord, or if a friend, by the surname only.

Women normally and traditionally take and assume their husbands' last name, title and status (if there's any).

The princess will take the title of her husband but will never lose her own title. Whatever title or status is higher or senior that's the one she would use.

Example:

An aristocrat His Grace The Duke of Brookshire married Princess Braguda of Commonwealth Realms. The Princess would assume the title 'Duchess of Brookshire" and some subsidiary title The Duke of Brookshire may have. But if the style of Princess Braguda is Royal Highness, she would not use the style Grace because it trumps the latter. The Princess would also retain her royal title and status being princess. She would be HRH Princess Braguda, Duchess of Brookshire, Viscountess Exeter, etc.

A princess would retain her title if she's European, no matter who she marries. In Japan, and possibly other parts of Asia in the past, the princess would lose her title and take on whatever title her husband had, if any.