I think this topic has come up before.
 
About 3 years ago, I switched all my brood chambers over from 10 to 9 frames.
This is recommended by Richard Taylor, Walter Kelley, and others in the books.
Basically, it makes removal of brood nest combs much easier.  In addition,
it gives the bees more cluster-space and improves ventilation.  (Not to
mention saving you 10% on the expense of frames, over time, anyway.)
 
Background:  In the late 1800's/early 1900's there was a famous commercial
beekeeper in the Northeast, named Moses Quinby.  He built and used a hive
considerably larger than the Langstroth hive.  Its frames were longer, and
a couple of inches deeper.  This shape, he felt, was more suited to the
natural laying pattern of the queen, and natural shape of the brood nest.
 
Later, Charles Dadant and sons used a hive called the Dadant, with
variations called the Dadant-Blatt (still used often in Europe) or Modified
Dadant. This hive used the deep Quinby depth, but the length of each frame
was the  same as we have in the Langstroth.
 
NOW, both the Quinby and the Dadant hives featured another important
difference, and that was they both used Quinby's recommendation for frame
*spacing*.
 
In nature the spacing of brood combs is normally around 1 3/8" center to center.
Sometimes it will be somewhat wider.  Quinby noticed this, and so designed
his frames to space 1 1/2" center-to-center.  The wide spacing, he was
convinced, was more beneficial to the colony, summer and winter.   Charles
Dadant, after many experiments with hives, concurred 100% with Quinby's
wide spacing.  So Dadant-hive brood frames are made to maintain this
spacing as well. The Dadant hive (still popular in France, and used at
Buckfast Abbey) is designed to hold 11-12 frames, as well as being deeper
than our Langstroth hive bodies.
 
Now, back to our Langstroth hive.  Even though the frames are made to space
the combs at 1 3/8", many beekeepers have found that manipulations are
speeded up considerably when you only use 9 frames for brood.  The added
space is not so much that the bees build great quantities of burr comb, but
it is of benefit in ventilation and even winter clustering.  Proponents
claim to see less swarming, do to the ventilation, and better wintering,
due to space for more clustered bees between each pair of combs.
 
According to Roger Morse at Cornell, the top-bar in
common use on our frames nowadays is a leftover from the section comb honey
era.  The hives were made with thick and wide top bars, which were supposed
to discourage the queen from going up into the supers.
 
Since this is not necessary anymore (queen excluder or super of honey will
keep the queen down below) we end up with quite tight bee-spaces between
the frame tops, across the hive.  This hampers bee movement, clustering,
and access to the supers from below. By using 9 fr insead of 10 in brood
chambers, you facilitate the movement of bees between chambers and up on
into the supers.
 
There is a bit more burr and brace comb with 9's, but not enough to justify
going back to 10's, IMO.  Some colonies just seem predisposed to build alot
of burr/brace comb like that, and others don't build much of it at all. If
you are careful about only leaving a smidgin of a space (1/8") between the
frame - shoulders, you probably won't have much trouble with burr combing
after all.