I have a few types of waterproof pants.
Different types perform in different ways. The waterproof membrane type (Gore-Tex, eVent, etc) all rustle when you walk - some more than others - and will leak wherever they are pierced. Apart from that they are totally waterproof when undamaged.
Some are designed to be a complete trouser/pant and some are designed to be an over trouser. Some are reinforced to give extra strength as membrane type garments tend to damage fairly easily. There are also very thin lightweight ones that are great for carrying but easily damaged, they also tend to be expensive.
Soft shell trousers are an interesting solution. I have a pair of Schoeller pants that are highly water and stain resistant. These pants are silent (no rustling) and they stretch. If they are pierced by something they won't leak at that point, unless it's a full on tear of course. One downside is that, unlike Gore-Tex, they aren't 1000% waterproof and will eventually let water through if you are in a heavy downpour for a long time.
Paramo have a similar solution to Schoeller, in as much as they are a soft shell product, and they are supposed to be excellent but I haven't personally tried them.
Another solution that I don't use but it is inexpensive is synthetic fabric that has been treated with DWR (water repellent coating). These garments will be highly water resistant at first and will fairly quickly (depending on usage) degrade in performance. After a few washings it won't perform very well but can be rejuvenated by using Nikwax waterproofing or a similar product. The advantage of this type of clothing is that it is cheap so not a big deal if it gets damaged.
There is also ventile but I haven't tried it so I can't comment. It is an expensive cotton material that, like Schoeller, isn't 100% waterproof but does offer a high level of water resistance and ought to be hard wearing.