Butterfly valves are great because of their simple and sanitary design. Unlike ball valves, butterfly valves can be completely cleaned and sanitized in place, without needing to take them apart for thorough cleaning. As such, I believe they are ideal for the wort/beer side of the brewing process. In my opinion they would ideally be used on fermenter outlets and on kettle outlets. They are not that good at finely controlling flow, so they perhaps are not ideal for controlling pump flow rates or for controlling flow through a sparge return on a mash tun or a tangential inlet on a boil kettle.
Ball valves offer good flow control but are a bit harder to clean. They are typically cheaper than butterfly valves. I would use them for controlling flow with pumps and on the water side of the brewery. Three piece would be my preference as they can be disassembled and cleaned, but the economy valves offer similar performance at a lower price.
Threaded fittings tend to be cheaper than sanitary fittings, but they must be disassembled after each use in order to properly clean and sanitize to the level of tri clamp fittings. As such, a threaded butterfly valve doesn't make much sense in my opinion.
My personal preference would be to not have any welded-on valves. I want to be able to remove any and all valves for cleaning and/or storage or to make way for other attachments. As such, my preference would be to have welded universal fittings, such as tri clamp fittings, that can be adapted to a variety of valves and attachments. NPT fittings are also common and popular, allowing for less expensive hardware to be used, but in either case, it is the fitting that is welded, allowing the valve to be removable.
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