Plastic grips have their place, but they're not the best choice for most recreational skiers. Their main advantage is weight—plastic is extremely light, which is why you'll find it on race poles where every ounce counts. They're also very durable and hold up well to abuse, making them common on rental and budget poles.
The downsides are significant for everyday skiing, though. Plastic conducts cold, so your hands will feel chillier on frigid days. It also gets slippery when wet, and offers almost no shock absorption when you plant your pole on hardpack. If you ski in cold conditions or tend to get cold hands easily, rubber or cork grips will be much more comfortable.
Plastic grips make the most sense if you're a racer chasing every weight advantage, or if you're buying budget poles and don't ski often. For regular resort skiing, rubber is a better all-around choice, and cork is ideal if you run hot hands or spend long days touring.