A wade fits closer to your horse. The tree is wider and flatter over the withers. It's rigged differently so that if you rope something heavy, it sucks down close instead of pulling sideways. It's flat rigged into the skirts, no "D" rings. It's narrower in the semarehan it looks, taking pressure off of the inside of your legs. If you have leg or hip problems, your leg(s) won't go numb from hours of riding. The stirrup leathers sit back and hang at a different angle, allowing you to easily 'post' a trot, a teqniqe not only used by the English dicipline, but also by open range cowboys who may ride 10 or 15 miles at a trot just to get to the cattle. Posting a trot is easier on you and a lot easier on your horse. The back of a wade is high and straight, keeping your posture more correct which in turn saves your back a lot and also helps you out a lot riding a buck, jump or stumble.
"Duck bill"? I assume you mean the horn on the wade. It's a 'slick horn' AKA 'post horn'. You usually don't use rubber on it. Wade is a buckaroo saddle. Usually, it's wrapped with mulehide, a hard grey cow leather strap, rough on both sides. After proper application and break in, it allows the rope dallies to slip. You usually take 3 to 4 deep fast wraps and 'play' your critter like a fish. Most slick horn cowboys ride with 60 foot of soft, 3/8" rope. Around Wyoming, Colo and Montana, you can buy it just about anywhere in bulk and tie your own knots. The big dally post makes it easy to to burn your wraps to in a hurry and the large size makes more friction that gives you more leverage on the knot end. It takes some practice.
The wade horn is usually straight upright with the cap not much bigger than the shaft. Called a 'dally post horn'. 'Duck bill', not sure. Maybe it is on some of the A fork rigs. Probably so you don't miss your wraps when you go to the horn. A fork is a buckaroo saddle too.
I rode a 40 wade for years, that's all I'll ride. Don't like A forks personally, rode 3 or 4 of them here and there. Either the wade or A fork will need bucking rolls put on. If they're put on correctly, they'll lock you in for just about any kind of storm. If not put on correctly, LOL, watch out

There's more, but I have a headache, slept 4 hours after 24 on the road and have to go back out in 30 mins.
Gotta go,
C.