I would NOT weld up an exhaust system, unless you've got problems that can only be solved by welding. Perhaps if the parts were Stainless Steel and will last the life of the car, or at least a decade, you will just have a tougher time repairing the exhaust later, when other pipes rust out.
If you are putting together a SS exhaust system, that will last for a decade or more, yea, I can see welding it all up and making it totally trouble free for that amount of time. In a decade, the clamp joint is more likely to fail than the rest of the exhaust.
The key element of exhaust work is what shape the end of the other pipes your joining the new pipe, and how well do they fit. If they have been severerly crushed by the last clamping together, they will be difficult to get apart, and can damage them taking them apart, meaning you have to get more pipes. You may need to reshape/repair the old pipes, there are tools to reshape the end of the old pipes back their original shape. You can rent/borrow the tools from places like auto-zone.
The big flat collar clamp? I think it would be superior, IF THE PIPES WERE DESIGNED TO USE IT, or at least they are perfectly straight, tight fitting and/or soft enough to be crushed in all directions. It would seal 360° around, and not make big crimps in the pipe, like the typical "U" Clamp. It would be a big advantage for hi-performance exhaust, because it would NOT create the big crimps in the pipe that could interfer with exhaust flow. Many companies use this type of clamp as OEM, but the pipes were designed to use them.
The "U" bolt clamps crush down one side of the outer pipe, forcing the inner pipe against one side and the crushed crimp on the other, to make a tight fit. If your pipes are real loose, pretty mangled up, etc, the "U" bolt clamp is probably going to make a better seal than the Big Collar Clamp.