There are many plastic label materials and each plastic has its particular characteristics. Temperature resistance is high for Polyester but relatively low for vinyl (PVC) for instance, but the reason for choosing one over another can go far beyond this.
A common reason for choosing a plastic rather than paper is to prevent water from getting into the label and weakening the adhesive. Another valuable property of plastics is their strength - a paper label would struggle as a luggage tag and yet a paper label would struggle to be as 'destructible' as some specially tailored plastics - providing tampering evidence.
Vinyl and Polyester can be specified with silver or golden 'Mirror Finish' lustre's too, for brilliant impact.