These two cheap bits of kit both fight the cold, but they fight it from opposite directions, and understanding the difference stops you buying the wrong one. A sleeping mat stops heat draining out of you into a cold floor — the ground pulls warmth away far faster than cold air does, which is why people who sleep on a floor in a power cut often feel colder than expected. An emergency (foil) blanket does the opposite job: it wraps around you to reflect escaping body heat back and block wind and damp.
Because they solve different problems, the strongest setup usually uses both together rather than choosing one. If you can only start with one, the right pick depends on whether your main issue is a cold surface underneath you or heat escaping around you.