The Cap and Comb of the 34C and 38C are identical, the only difference is in the length, weight and balance of the handle. But I wouldn't expect them to shave much differently. I used the 34C for years. It is a fairly mild razor. The benefit of an adjustable is you get to try various level of agressiveness, but you are still locked into the same geometry. Each razor is different, and the geometry will vary from razor to razor. So unfortunately, if one isn't giving you the shave you wanted, you may need to try another, and another, and another until you find what works the way you want it to. My favorite Adjustable is the Gillette Fatboy (a vintage razor). I did try the Progress, and I did not like it. I do, however, like the MERgress, which is a Progress with a few modifications made to it. Not sure why it's that much different, but it is. I hated the Futur when I tried it, way too aggressive for my face.
I personally do not prefer adjustables to traditional DEs. When I use an adjustable, I get it dialed in to the level I prefer, and I leave it there, never to be adjusted again. I'd actually just prefer to use a regular DE that is suited to me.
The thing I'm keying in on is that you said your beard comes off quicker with a more aggressive setting (presumably) in the adjustable than the mild 34C head, which makes sense.... but you're not getting a closer shave. That could be the razor's geometry, but my gut is telling me that maybe you need to explore different blades. Each blade will shave differently as well. Each has their own grind, sharpness, and geometry. With a heavier beard you may need a sharper blade. I'd recommend trying a Feather blade, which are among the sharpest.
SV is a great soap with great scents, but there are plenty of less expensive soaps out there that work just as well. The good news is that SV soaps last forever, so they end up being economical in the long run.
My personal favorite is CBL Soap, which is another great artisan vendor of the TSC.
