As a fan of neither but practitioner of both, I can say that in clay
soil none of the above works for me! When it would be the best time
to hoe (ie, when you are doing more cultivation than hoing small,
eensy teensy weeds) the ground is too wet to work or dry/tough as a
parking lot. As in no way would a tiller or a hoe work at all.
Raised beds, yada yada. It's being amended for several years now with
all the right organic stuff, just swallows it down and seems to not
make much difference in soil quality. Peat, leaves, straw and grass
clippings in vast quantities, and seasonal application of aged manure,
sand and sand and sand.

And the reverse is also true, when the ground has dried to the point
it can be worked with a hoe, the weeds have a good head start on me.
My window seems to be quite small where the ground may be worked, and
often I'm not prepared to do the work at the most propitious time.

This year I am taking a stand with a grub hoe - adze or mattock - that
weighs in at 8-12 pounds and plan to clobber the weedy patch - er,
garden - before the things are 8 foot tall again. I have started
layering in bales and bales of straw. My short potato row took 1.5
bales of straw, but it looks promising - the only weeds left are the
ones poking up on the edges, not around the potato plants. They are
somewhat easy to pull, as that soil was amended with 6-8 inches of
wood chips several years ago and they have turned into a delightful
almost-soil mixture. If the straw lasts longer than the season I will
try to till it in and get more straw next season. $7/bale but the
bales are larger than "normal". I don't know exactly what that means,
but my experience prior to this was the smaller bales, and 7 would be
too high a figure for those. The ones I mention are at least 1.5
times the size of those small regular bales.

The corn was a different tale, as I layered in some bags of leaves I
conned - er, received from a friend. I think these were kinda acidic
in quantity, as the seedlings have not done much at all for 2.5 weeks
now. They might be past the crucial stage as they are beginning to
turn from a sickly yellow to a nice dark green. They have been
mulched with a layer or 3 of newspaper, followed by a layer of leaves,
topped with 3-5 inches of straw. Weeds are coming up through that
like it's hard to believe - wisps of grass and creeping charlie and
ragweed. Not supposed to, but there you are.

I think back to the days of my misspent youth when the garden at the
old home was really nice and friable and could be worked with a hoe -
that was good soil, and I was too young to appreciate it.

Definately takes longer and more effort IMO pulling the weeds by hand
one handful or plant at a time than it takes hoeing.