When it comes to fishing line and chasing walleye in our lakes, I choose both braid and mono. Braid is a great choice for trolling, with my favourite being PowerPro in 15 and 20 lb test! Be it trolling a lure, or running bottom bouncers on bottom with spinner rigs, braid affords me a direct connection, with no stretch, to my gear. It also means more positive hookups with biting fish. That is, more of the forward energy of trolling is transferred into setting the hook when a fish bites, opposed to mono, which is stretchy and results in less hooking power. It also means when I hook a fish, I have the line strength to pull it in, quite handily if needed.
But, when it comes to jigging, I prefer mono. I like the suppleness of the line, plus I feel that thin mono does not get dropped as often as thicker braid. I say thin mono, because I am typically running 6 lb test. Because mono is stretchy, when I feel a bite, I reel fast until I feel the weight of the fish, then I set the hook. If I've sharpened my hooks, the lighter mono should still have no problem setting the hook.
As for matching rods, I choose a medium to medium heavy rod for braid. For mono I will use a medium to medium light rod. Most rods I run are 6 and half to 7 feet. When paired with a good rod both braid and mono have their advantages, which is why I will have both with me when I head out walleye fishing.