Both are common add-ons to a London trip, but they pull in opposite directions — Manchester is an industrial-turned-creative northern city built around music and football, while Oxford is a small, ancient university town built around eight centuries of academia.
Manchester's identity is industrial and civic — Manchester Town Hall's Gothic Revival grandeur, plus modern venues like Factory International. Oxford's identity is entirely academic — the Radcliffe Camera's domed reading room is the most photographed building in a city built almost entirely of honey-colored college architecture.
Manchester's Museum of Science and Industry (MOSI) and National Football Museum reflect the city's role in the Industrial Revolution and the modern game. Oxford's draw is different entirely — touring Christ Church College and the Bodleian Library, plus the free Ashmolean Museum, gives access to working university buildings rather than exhibits about the past.
This is Manchester's clear edge — Old Trafford Stadium (Theatre of Dreams) and Etihad Stadium make it one of the best football pilgrimage cities on earth, with stadium tours available even outside match days. Oxford has no equivalent; its closest thing is rowing on the river Isis and a much quieter, academic sporting culture.
Manchester is a full city in its own right, with shopping, nightlife, and music venues that reward a multi-day stay. Oxford is compact enough to see in a day, and its best move is treating it as a base for Blenheim Palace and other Cotswolds day trips rather than a standalone destination.
Choose Manchester for football, music history, and a real working northern English city. Choose Oxford for university architecture, a walkable half-day or day trip from London, and easy access to the Cotswolds. They're not close to each other (about 3 hours apart), so most travelers pick based on which fits their London itinerary rather than combining both.