Back when, screw builds were a means of building with out having to press out the barrel pin and barrel from the front trunion in order to re-rivet it back into the new receiver. You then had to repress the barrel back into the trunion and reset the pin. A fair bit of work for sure. I am a bit of a purist and wanted my guns to be as original as possible. I made a rivet tool out of a set of bolt cutters for the front trunion and a rivet press jig for the rear one. As I have access to a 50 ton press the barrel and barrel pin press out was not an issue. The pins can be a hard go depending on the kit used.
If you get a kit with a cut barrel your going to have to press out the barrel stub and pin anyway and at that point would be able to do a rivet job. You will have to press the new barrel into the the trunion. Also you will have to set the headspace in the process of redrilling and pressing in the new barrel retaining pin.
I cant give an opinion on the screw build method as I have never done one or even shot one. Either way seems to have its challenges. Thats what makes it worth the time and bucks to me. Lot of satisfaction in shooting something you put together yourself.