These two series were produced independently of each other by completely different companies. I’m sure it’s just a coincidence that they wound up airing in the US at roughly the same time. But having seen them roughly back-to-back, it’s inevitable that they will be compared.
Each series concerns the early reign of a young, under-prepared girl as Queen of England. Each shows us the young Queen developing a working relationship with various Prime Ministers, handling the unpopularity of her foreign-born husband, and dealing with the fact that, despite the trappings of privilege, her life is no longer totally her own. Each features an alumnus of Dr. Who is a leading role (Matt Smith as Prince Phillip; Jenna Coleman as Victoria). Each features English actor Alex Jennings as the Queen’s busybody uncle (King Leopold / Edward VIII). Each has a subplot involving the obscure Royal Marriages Act, which seems to have no other purpose than interfering with royal romances. Each is shot in beautiful period-appropriate locations, with beautiful period-appropriate costumes. And each features a rather surprising rat in the Buckingham Palace kitchen (I think it’s the same rodent, but I wouldn’t swear to it).
Victoria is a little soapier, with some subplots involving “downstairs” characters. They don’t really add much to the plot, although one relationship is very sweet (it involves the pastry chef). In The Crown, the senior members of the royal staff, themselves children of the aristocracy, are treated like servants, and the actual servants are treated as though they don’t exist (which I suspect is closer to the truth).
Victoria also has a more romanticized vision of the monarchy. The Crown is neutral on the subject, but anti-monarchists will find plenty of ammunition.
The Crown probably has a stronger cast (Clair Foy as Elizabeth, John Lithgow as Churchill), but Rufus Sewell as Lord Melbourne is pretty good too. The Crown also has better writing, and grittier characters, but perhaps takes itself just a bit too seriously. Victoria, while lighter fare, is more fun to watch.