If you're talking about using old school mounts with a dovetail in the front and windage adjustments in the rear I'd not touch either of them with a 10' pole. Those were designed for rifles manufactured 75-100 years ago that often had the mounting holes drilled incorrectly due to the technology of the day. They allow you to get the scope mounted directly in line with the barrel even though the mounting holes may not be. On a modern rifle they aren't needed and there are far better options available today. But lots of folks still use them simply because that was what grandpa used without realizing there was a good reason why grandpa needed them. We don't need em.
A one piece base does nothing to stiffen the action, but in some cases are a good option. If you want to mount a Picatinney rail and use rings with a cross slot that is a viable option that gives you more options for scope position. This is my choice for a target/tactial type rifle.
But on a hunting rifle I prefer 2 piece bases and the Talley Lightweights are at the top of my list. They are not only about 1/4 lb lighter than old school windage adjustable mounts, but they are stronger. Using 2 pieces keeps the ejection/loading port open and more accessible for loading or clearing jams and cleaning. There is nothing at all wrong with the 2 piece Weaver, or Weaver style bases with cross slots. Even the Weaver rings are functional, if not utilitarian looking. I like the Burris Zee rings better and they are my 2nd choice behind Talley.
The DNZ rings are available now in one or 2 piece. Nothing wrong with either of them, I just like the looks of Talley or Burris better.