Glass : can only be molded at very high temperatures. It completely melts/liquifies at approximately 1400 °C to 1600 °C depending on the composition of glass. Glass is made from a variety of substances, depending on the intent of use. Mostly sand, lime and soda are what most glasses are made of. The melting point for ordinary glass is around 550 degrees centigrade (Celsius) or1020 Fahrenheit.

https://en.wikipedia.org/wiki/Glass

Plastic :Of the six commonly recycled plastics, four can withstand temperatures of 100 degrees Celsius (212 degrees Fahrenheit) or above. According to Machinist Materials, polyethylene terephthalate -- PET, or recyclable 1 -- has a melting point of 255 degrees Celsius (491 degrees Fahrenheit). High-density and low-density polyethylenes -- HDPE and LDPE, or recyclables 2 and 4 -- melt at 130 degrees Celsius (266 degrees Fahrenheit) and 120 degrees Celsius (248 degrees Fahrenheit), respectively, according to Dynalab Corp. Most cups designed for hot liquids are made of polypropylene, or recyclable 5. This plastic's melting point is 170 degrees Celsius (338 degrees Fahrenheit). Finally, the range of melting points for recyclable 6 plastic, formally known as polystyrene, is 100 to 120 degrees Celsius (212 to 248 degrees Fahrenheit) according to T.C. Forensic.

One commonly recycled plastic, however, could be melted by hot water. According to T.C. Forensic, some polyvinyl chloride plastics -- PVC, or recyclable 3 -- melt at as low as 75 degrees Celsius (167 degrees Fahrenheit). PVC is largely used in construction applications, so you're unlikely to encounter it holding a beverage.

https://en.wikipedia.org/wiki/Plastic

So yes, plastic metls faster.