I would guess the D200 might do better but I have nothing to support it.
Good question.

The main differences between a D80 & D200 are the ability to meter with
old lenses & the improved accessibility to control features with knobs &
buttons versus menu diving. Stuff like AF & AE settings can be changed
with the flick of a finger with your eye to the lens, changing modes,
more info in the finder, etc... long list. If you don't think you'd use
those manual controls, don't like the extra weight & aren't interested
in old manual focus lenses then the D80 is for you.

Beware the rash opinionated judgements but here's a comparison with some
useful charts:
http://www.kenrockwell.com/nikon/d80/vs-d200.htm

what you need is a larger aperture lens.  The focus hunts
because the AF sensors don't get enough light to decide on
a focus point.

With the same lens and lght?  Not really: the problem is not
in the camera.

the d200 and d80 are supposed to focus faster.  But again, that
depends a LOT on the lens: an AF-S lens will focus much faster than
an AF lens, with any camera body.

I'd suggest you spend some time considering upgrading your
lenses rather than coughing up for a "pro" body.  You won't gain
that much from 6MP to 10 anyway and both will let you
produce poster size prints.  What the 10MP will give you
is a bit of leeway in cropping.  Is that enough to invest in a new
body?  You can answer that, I can't.  Rest assured: both will
produce excellent posters.

Lenses matter a lot more for larger photos than megapixels.
There is a world of difference between an AF-S 70-200 f2.8 VR
and a vanilla 50-200 f4-5.6.  And it's not just letters.

Ken's site is good for lens evaluations but bear in mind
he's looking at them from the point of vue of the average snapshot
punter.  As such he might recommend what a more serious
photographer might not touch at all.

There is a reason why better lenses are more expensive and it
has nothing to do with average size photos. If you want to avoid
problems later on, look at any lens that has a constant max
aperture of around 2.8: these are usually the better gear and will go
a long way in avoiding focus problems.  Also, consider AF-S and
VR: both can be important.

Don't forget a tripod or at the very least a monopod: either can save
you a lot of "out of focus" shots.