What are the advantages of buying plastic over metal tire levers? (or vice versa).
Which ones are easier to use?
It largely depends on the usage you want to make of them and the particular tire/rim combination you use.
Plastic levers are usually small and lightweight, and if they are of good quality, they are enough for most tires that are properly fitted to the rim. I mention this because sometimes, rims and tires can physically differ from the nominal size they bear in their labels, so a tire may fit way too tightly in a rim. Other times, the wire collar in the bead may be too stiff. These two situations make them very hard to pry out, thus a tiny plastic lever may break, however, this is a rather rare case.
Small and light tire levers are ideal to carry in the emergency tool set for on the road or on the trail repairs. And for most cyclists that may now and then perform a tire swap at home.
Metal tire levers may be heavier or more expensive (due to being manufactured from fancy metals), and usually are bigger and better suited to shops where several tires are swapped or repaired by the same user each day. In this situation the large lever makes the work easier by providing (you guessed it) more leverage. They are also well suited for the situation described above, specially if for any reason you are forced to almost always use a tire that "almost fits".
Another reason to prefer plastic levers is that it is very difficult to damage a rim or a tire bead, while a poorly polished metal tire lever, or a poorly used one may easily damage the rim or the tire.
In the other hand, I would advise not using plastic levers that are too flexible or too thin and brittle.
Keep in mind that there are also levers made of a metal core covered in plastic. They are kind of in the middle of both sides.
Note: I consider tire levers survival equipment, along with patches and glue and/or an extra tube, thus, if first time buying tire levers, or first time buying that brand/model, I strongly advise testing them at home before engaging on a long tour alone or you being the only one carrying emergency items like these, so you don't get stranded in a far place with a puncture and a pair of failed tire levers...
Good plastic levers are wide, made of hard but resilient plastic and work well. Being wide means they are stronger than a narrow plastic lever without being thicker (which would make them harder to push under the bead). The S-shaped hook on the end grips the bead well and the other side of the S hooks onto the rim, so the lever stays in place as you lift the bead. I use both these brands and don't really have a preference - there's a Schwalbe one on my keyring and Michelin ones in my toolkit. When I worked in a bike shop we used Michelin ones and they lasted for years of daily use. If you like the hook on the end, Schwalbe has that.
There are a wide range of poor plastic tyre levers available. Many are narrow but thick, making them hard to use, or lack the S-shape on the end making it hard to keep the lever correctly placed on the rim - as you pull the bead up the lever often slips toward the rim, making your leverage worse and often breaking the lever. The one pictured below is only slightly better than a metal screwdriver.
Metal tyre levers are often similar to poor plastic ones, as above. They have the added problem that if you twist the lever as you're using it much of the force on the rim is applied at one side of the lever - effectively a point force. Since it's a hard steel lever applying force to a soft aluminium rim, you'll often dent the rim by doing that.
There are good metal levers available, for example Park make one (below). Note that it's about 20mm wide where it meets the rim, and it has the S shaped hook.
In my experience people often ask about tyre levers when the problem they're having is technique. So I've asked a question about that
Plastic tire levers are more likely (than metal) to break. Especially over many uses, they'll eventually fatigue. They also tend to flex more.
Metal tire levers are more likely (than plastic) to damage the wheel rim.
It's also possible to get plastic-coated metal levers that get the best of both worlds.
Unless you're in a shop and using the levers dozens of times a day for years, you might as well just get the plastic levers, because they're inexpensive and the differences are fairly small.
Neither is really easier to use than the other. Length of the lever makes a bigger difference than material, and having a notch on the back end of the lever that can hold onto a spoke can be handy when dealing with a tight tire, since it allows you to keep a lever in place without using your hand.