The main differences between the protein in meat and plant foods are the range/amount of amino acids they contain and how well they’re digested.
Amino acids are the building blocks required to make muscle, skin, hair, hormones, etc. and they must reach your blood before they can be used. More of the amino acids found in animal foods than plant foods do this.
Additionally, animal proteins contain all nine essential amino acids needed for health, while some plant foods are deficient in one or more, e.g. grains lack lysine while legumes lack methionine. On this basis, meat could be considered better for you.
However, it’s perfectly possible to obtain sufficient protein for health from vegetable sources. Consume quinoa and soya regularly, as they both contain all the essential amino acids, and include a variety of different grains and legumes over the course of a day. It’s also good to aim for a slightly higher daily protein intake overall, e.g. 1.4g/kg of body weight vs 1.2g/kg for a meat eater, to allow for the reduced digestibility of plant proteins.