How EXACTLY are different-sex siblings related as much as same-sex siblings?

They are not EXACTLY related!

Humans have 46 chromosomes in each somatic (body) cell.  These contain
the genetic code (DNA) that controls the appearance, etc of the
individual.

Since gender is determined by whether a person carries the two
chromosomes XX (female) or XY (male), two people of different gender
would have that 1 chromosome in 46 be different.  So in theory,
different sex siblings are slightly more genetically different than
those of the same sex.

However, because human DNA and chromosomes are based on an independent
assortment of 23 chromosomes from the mother and 23 from the father,
siblings tend to be more closely related to one another than they
would be to any other human being.

Basically, there's about a 50-50 chance for the siblings to be boy or
girl, but in either case their DNA is going to be very similar.

Dear arkin,

I just wanted to add a little to what Loudnotes said about genetics. 
If there was no independent assortment of chromosomes (as Loudnotes
describes) then brothers would be more similar to one another than
would a brother and sister.  However, since human chromosomes do
independantly sort with each fertilization it is possible for a
brother and sister to have all the same chromosomes alike except for
the X or Y that they got from their father.  Also, it is possible for
two brothers to have gotten all different chromosomes from each other
except the one Y from their father.  Essentially, since gender is
determined by the single X or Y supplied by the father, two brothers
could share one chromosome while having 45 different from each other. 
Conversely, a brother and sister could share the same 45 chromosomes
and have only one different from each other.

Both of these scenarios are unlikely, as there is some amount of
linkage between certain chromosomes.  And, it is improbable that two
siblings would share either all or no chromosomes.  However, it is
possible.

If that satisfies your question, I can post it as an answer.

I hope it helps.
Peggy_bill