Though examining the character relationships, please compare The Taming of the Shrew and 10 Things I Hate About You.Please give me textual...

This question could  make quite an extensive essay, so
I'll cover two relationships and point you, hopefully, in a useful direction.  Also,
since you don't distinguish, I'll be using the characters from 10
Things, the TV show.

The first major difference
between Kate and Petruchio in Shrew and Kat Stratford and Patrick
Verona is the way they interact.  In the play, Petruchio determines to make Kate his
wife, regardless of how she feels about it.  He gives the reason of
money:

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...and, therefore, if thou
know

One rich enough to be Petruchio's
wife...

She moves me not...

I
come to wive it wealthily in Padua. (I,
ii)

But he also seems excited
by the challenge posed by the wildcat Kate.  So, he meets Kate and directly confronts
her and tells her she will be his wife, whether she likes it or
not:

Thus in
plain terms:  your father hath consented

That you shall be
my wife; your dowry greed on;

And will you, nill you, I
will marry you. (II, i)

So
the die is cast early in the play, and Kate is resistant the whole way.  When Petruchio
says that they'll marry on Sunday, she retorts:

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I'll see thee hang'd on Sunday first. (II,
i)

While Kate and Petruchio,
from the moment that they meet are struggling over the questions of first betrothal and
later appropriate behaviour between husband and wife, Kat and Patrick are simply
students in high school, who are attracted to each other, but always seem to be at odds
over something.  This sort of cat and mouse tension works well for a TV show that must
run over many episodes, and also displays the awkwardness  that can exist between
teenagers when it comes to love.  They don't come anywhere near the life-changing topic
of marriage, and are pretty much confined to the common issues facing teenagers in
today's society.

The other major relationship that the TV
show 10 Things and Shrew portray differently
is Kate and Bianca, or Kat and Bianca.  In Shrew, Kate really has
no interaction with Bianca, save to tie up her hands and try to make her confess which
of her suitors she loves.  When their father comes in on this, he scolds Kate and
comforts Bianca.  Kate replies:

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...Nay, now I
see

She is your treasure, she must have a
husband....

Talk not to me, I will go
weep,

Till I can find occasion for revenge. (II,
i)

In 10
Things, these sisters have different personalities, but they ride back and
forth to school together, and sometimes cover for each other when one disobeys the house
rules.  Kat might not really understand why Bianca values the friends, etc, that she
does, but their relationship is nowhere near as hateful as the one in Shrew
appears to be.  Also, the above text suggests that Bianca is their father's
favorite in Shrew, while in 10 Things, it
seems that their father really admires Kat's quirky spirit best.