read strunk's rule on this, but still not sure if i gor it right. Is "compared with" used for contrasting things with differences. Is "compared to" used for comparing similar things? Please give examples for illustration.
What is more correct: "The agriculture sector grew 50% this year compared to last year." "or compared with last year."
What is more correct: "The agriculture sector grew 50% this year compared to last year." "or compared with last year."

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Honestly, Strunk's rule-- and Fowler's before him-- are ignored by most every native speaker now alive. If you must differentiate, use with for more extended or in-depth comparisons, and to for simpler ones.
Welcome to the Forum.
My dictionary says that compare followed by to often expresses similarities, and that with often implies a greater degree of formal analysis. That sounds about right to me.
However, it goes on to note that in current usage, to and with are often interchangeable. So, I would consider Strunk rather out-of-date on this.
What is more correct: "The agriculture sector grew 50% this year compared to last year." "or compared with last year." Either sounds OK to me.
[As a minor comment, it's good to get in the habit of using capital letters to start a sentence, for proper names and for the pronoun 'I'.]
Best wishes, Clive
compare with; compare to
The usual phrase is compare with, which means "to place side by side, noting differences, and similarities between":
Let us compare his goals with his actual accomplishments.
Compare to = to observe or point only to likenesses between:
The psychologist compared this action to Hinckley's assassination attempt.
Garner, Modern American Usage, p. 167
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compare
. verb 1 (often compare to/with) estimate, measure, or note the
similarity or dissimilarity between. 2 (compare to) point out or
describe the resemblances of (something) with. 3 (usu. compare with)
be similar to or have a specified relationship with another thing or
person.
Compact Oxford English Dictionary
http://www.askoxford.com/concise_oed/compare?view=uk
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CPR, Bracknell, UK.
Shall I compare thee to a Summer's day?
Thou art more lovely and more temperate:
Rough winds do shake the darling buds of May,
And Summer's lease hath all too short a date:
Sometime too hot the eye of heaven shines,
And oft' is his gold complexion dimm'd;
And every fair from fair sometime declines,
By chance or nature's changing course untrimm'd:
But thy eternal Summer shall not fade
Nor lose possession of that fair thou owest;
Nor shall Death brag thou wanderest in his shade,
When in eternal lines to time thou growest:
So long as men can breathe, or eyes can see,
So long lives this, and this gives life to thee.
Sonnet #18
I rest my case
Beautiful, of course.
But art thou suggesting that we should all be using the same grammar today that Shakespeare used in the 16th./17th. century?
Best wishes, Clive