Manchester vs Leeds for students
General comparison of student life in the two cities.

Both Manchester and Leeds are major university cities with similar student populations and established student cultures. Manchester's universities are integrated into the city - campus is spread across central Manchester. Leeds has a more traditional campus-based setup. Manchester has a stronger music scene and slightly lower cost of living; Leeds is known for nightlife and has a more compact city centre. Both have good transport connections, good libraries, and range from north to south England.
The student accommodation areas differ. Manchester has south Manchester (Fallowfield, Rusholme, Withington) as the traditional student belt. Leeds' student accommodation is spread across different areas - Hyde Park, Woodhouse, Headingley. Manchester feels more ethnically and culturally diverse; Leeds feels slightly more compact. Both cities are close to transport links to other parts of the UK - Manchester to Liverpool and beyond west; Leeds to York and north. Neither has a significant cost advantage over the other.
The choice between Manchester and Leeds often comes down to the specific university and course, the campus environment you prefer, or personal connections to the city. Spending a day in each city if you can helps. Talk to current students at each university. Both are good cities for student life - your experience will depend far more on your own engagement and the people you meet than which city you choose.