Here are a few of the main differences between using glass or plastic as storage containers.
1) Glass will be hard sided container and plastic can be either soft (bag or film) or a hard sided tub. You most likely knew this one but the stiffness of a container can make a difference. Both types can be made air tight but you can not (easily) take all of the air out of a glass dish or plastic tub where you can from a bag. Removing the air from around food before freezing it can help to prevent extra ice crystal formation. Limiting the contact of air with food can keep it from drying out. They also keep out the gasses given off by some foods when they begin to break down that can start other foods begin to degrade. Glass lids work OK for this but not as well as some plastic lids.
There are plastic bags for vegetables that have little holes in them that claim to balance the moisture level inside and keep them
2) Glass containers usually are better at holding heat which is good to keep things hot or cold but also means that a warm glass dish will take longer to cool down. A plastic tub is not quite such a good insulator but will hold some heat or keep things cool for awhile. Things in plastic bags or film will change temperature the fastest. If you want to limit the growth of bacteria it is best to cool the food quickly.
3) Glass and plastic containers can interact with food differently on a chemical level because of the difference in their own chemical structures. Glass is mainly made up of silicon dioxide (SiO2) or melted sand. Depending on the type of glass other chemicals (like calcium, sodium and boron) may be present in the glass. If liquids are stored in glass, a very small amount of these chemicals can leach into the liquid.
Plastics containers are made of long chains of carbon and hydrogen. The specific structure of those chains changes depending on what type of plastic it is (cellophane vs. polyethylene for example). To help give useful properties to plastics they often contain additives which are usually small molecules that sit next to the long carbon chains. These additives can do things like make it harder for bacteria to grow on the plastic or make it possible to form the plastic into a useful shape. Mostly these additives stay in the plastic because the like sitting next to the carbon chains much better than swimming around in water, but small quantities of the additives do leach out of the plastic. Some of them are OK and some are not. Usually, leaching increases with temperature since molecules can move around more.
Hope this helped.