I do both. Both methods have their advantages and drawbacks. With multi-material construction, such as damascus bolsters over steel liners for example, you're saving a lot of material by soldering the bolsters, and can potentially use completely different patterns.
Most of my single material bolsters/liners I mill integral these days, but there's a practical limit to how thin you can get the liners. I like my liners around 0.040" thick, and that's very difficult to mill that thin, especially on single ended bolsters, because work-holding the liners gets really tricky. Most people that mill integral bolsters, leave them MUCH thicker.. Once you get down below 0.060, most materials will want to warp up into the cutter, I've ruined many trying to figure out a method of getting them as thin as I want. You can also surface grind integrals, but the same caveats apply, after a point, even the best magnet has difficulty holding the liners, stainless especially.
There are also caveats to getting them lined up correctly, I use a shop built jig to hold my already shaped and fit liners. Either way, it still introduces a lot of stress into the liners, and there's usually a fair bit of warp coming off the mill, right at the liner/bolster transition, and it's a tricky spot to straighten completely, if not completely straigthened, this'll translate to being able to see light around the spring between the liners if held up to a light source.
With spot welding or hard soldering (brazing) you can much more easily go with super thin liners (most people don't do them as thin as me, so it's not an issue), and if setup correctly, I get almost no warp from that process.
However, I do prefer integrals, and you can do some interesting things with different shaped cutters for the scale to bolster transition. I think many customers consider it a feature, but it's certainly not the only or "right" way to do it. Just like pivot bushings, or pin vs screw construction.
Regardless, like everything, if you truly want to have the range to construct anything, from any material, it's advisable to learn to utilize all the tools at your disposal.