They solve different jobs
A widget is a durable surface for information you want available whenever someone looks at the Home Screen or supported Lock Screen placements. A Live Activity represents an active experience whose state changes over time.
Choose a Live Activity when the activity itself matters
Live Activities can appear on the Lock Screen and around the Dynamic Island on supported iPhones. They are the better fit when the person has deliberately started or is following a live session and timely state is part of the experience.
Choose a widget for the everyday snapshot
If the job is simply “show me my current walking status when I glance at my phone,” a widget can be the calmer persistent surface. A strong step app can use both without making either surface pretend to be the full application.
Primary sources: Apple — ActivityKit · Apple — WidgetKit