On Wednesday, November 22, 2017 at 11:45:10 PM UTC-8, OFWW wrote:
I was just going through a few of my hand planes ...
I tested a few and was amazed at how smooth the wood was after it was
planed. Especially on 3/4" edges. I don't remember sanding getting
them that smooth.

My question is, when using my router to do the same thing I don't ever
remember the shapes being that smooth, so do the hand planes cut the
shapes as smooth as a flat plane does?

Routers (especially with carbide bits) have a less acute cutting edge than
the iron (steel, actually) of a plane. Yes, the cut of a plane is smoother,
but it also depends more critically on the wood grain and toughness.

Some edge ornamentation uses high-angle planes which are less sensitive
to grain. The most extreme are called 'scratch planes' because the edges are
as blunt as a carbide router bit.