the damage displayed in your character screen is your damage per shot.
the damage you deal with the throium weapon is higher because you fire
faster.

The Thorium rifle's damage *is* higher.  The range you're looking at is the
damage output of each shot.  But since the Thorium rifle is faster, it does
more damage over time than the Mithril.

in addition to that, if that already confuses you, wait until lvl 70 when
the correct weapon speed (to fire at a steady:auto 1:1 rotation) has to be
perfect in order to deal the maximum amount of damage over a period of
time, which will let you choose a lower dps weapon over a higher one just
because of the speed.

(this is offtopic)

might switch to marksman then ^^

As has been said by the other posters, the Thorium Rifle's damage
output IS higher :).  DPS is really the number you want to be looking
at.  The actual damage per shot done by the weapon (which is what
you're looking at) isn't really all that important.  Your damage
output will be a function of the damage per shot combined with how
often those shots are taken.

To simplify (and exaggerate numbers for a point), lets say your
Thorium Rifle hits for 1 damage per shot, but youre Mithril Rifle hits
for 2 damage per shot. One would think that the Mithril rifle is doing
twice as much damage at first glance.

Frequency wise though, your Thorium rifle fires every 2 seconds and
the Mithril rifle fires every 5.

Over 20 seconds, the Thorium rifle has done 10 total damage.  The
Mithril rifle has only done 8.

If we expand that to say, 10 minutes, then the Thorium rifle has now
done 300 damage, while the Mithril rifle has only done 240 damage.
The lower damage shots hitting more frequently turn out to be better.

As Mark alluded to, as you level up and get to end game, with a BM
spec this will become more complicated.  You'll have to turn down
faster weapons (usually anything under 2.40 speed or so) even if they
do more DPS, because a high speed bow can start to "clip" your special
attacks so that they don't start and end between auto shots, and so
their affect on your rotation will lower your DPS even though looked
at independently the bow appears to be great.

Mike