Baltic vs. Veneer Birch Ply

I’ve done a few projects now using birch plywood. For the first one, I built the carcases for my kitchen cupboards out of non-baltic birch ply that came in 4×8 sheets from my lumber store (not the big box). The quality of the interior layers was not spectacular but it didn’t give me pause from a stability perspective and the veneer layer looked nice. For my next project, I spent the money on Baltic, which looks really nice and solid and consistent. The thing I’m struggling with, though, is that while the internals of the Baltic birch are really nice, the veneer on the lower quality stuff looks nicer. It’s a thinner layer, but it’s smoother and more consistent (at least as long as I cherry pick good pieces). The baltic is rough enough that I had to sand a significant amount of wood off the top layer to get it to a smoothness I liked and it still doesn’t look as nice.

So my question is: is this just how it is? Or is my lumber store just carrying a lower grade of Baltic Birch? Or do I just have to put my own veneer on it if I want it to look nicer?

-- Andrew