Neolithic people were farmers and Mesolithic were hunters.
Neolithic people lived in 7000 BC and Mesolithic lived in 3500 BC.
Meso means middle, so Mesolithic was middle stone age and Neo means new, So Neolithic was the newer or more recent.
Neolithic people feed more on cereals and other farmed crops while Mesolithic people feed on meat.
Making pottery and the beginning of metal working is seen in Neolithic period. Use of tools made of stone is seen in Mesolithic period.