In a nushell...
On the road, the Weber has substantially better acceleration and top end than the smaller, stock carb. Offroad, the stock carb performs better on steep angles.
The stock carb, when it is relatively new, will run great for a long time. However, once it starts have problems, they can be very hard to diagnose and fix. The Weber is not as trouble free as the stock carb, but it is very simple and easy to work on.