Two philosophies
Zonal marking defends space: each defender owns an area and passes runners on. Man marking defends people: each defender owns an opponent and follows him. Zonal keeps your shape; man marking keeps their star quiet - and drags your shape wherever he goes.
When man marking earns its risk
Man marking is a scalpel for one problem: a single dangerous creator, typically a CAM, in a team that otherwise threatens little. Against fluid front threes or teams that rotate positions, man markers get pulled across the pitch and leave motorways behind them. If you cannot name the one player you are marking out, you want zonal.
The hard rule
Never combine man marking with the offside trap. The trap requires a line stepping together; a man marker tracking his runner breaks the line and plays everyone onside. This is the single most common self-inflicted wound our engine flags in tested tactics.