I had a big chief smoker for years. Simple, works fine, all you need for occasionally smoking fish a few times a year.
That being, said I got a Bradley smoker last year and wish I had years ago.
The Cheif has a simple on or off element, so the temperature is what it is. This makes smoking a little more weather dependant. The Bradley has an adjustable element and a thermometer built into the door so you can control the temp based on what you are doing. You can even crank the heat up enough to cook things. The Cheif is simply an aluminium box while the Bradley is insulated and seals well which keep the smoke and heat in better. The Chief requires you to take the front off to change chips (or at least open the trap door in some models) losing the smoke you have built up. The Bradley has a stack you fill with pucks that then self loads automatically every 20 minutes a new puck onto the element and then pushes the spent one off and into a bowl of water to extinguish it. You never need to open the door and lose you smoke and heat to change chips, it's a pretty slick setup. With the Chief you can use whatever wood chips you want to fill the pan with, but the Bradley requires specific pucks. The pucks are more expensive than a bag of chips, but they smoke quick and extremely well and are available in pretty much any flavor that you would want.
There is nothing wrong with the Chiefs, they are good for the occasional smoker and mine served me well for many years and fish. The Bradley is definitely a very nice unit and a step up. The only cons are the initial price and slightly higher expense for the chips.