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Could you explain the difference between these sentences? Which are more common?

1. Her hands are rough like a peasant’s.
2. Her hands are as rough as a peasant’s.

1. I’m hungry like a wolf.
2. I’m as hungry as a wolf.

1. The water in the swimming pool is cold like in the sea.
2. The water in the swimming pool is as cold as in the sea.

1. It’s damp here like in a basement.
2. It’s as damp here as in a basement.

Thank you in advance.
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Both patterns are common. I'm not sure what you'd like to know about them.

I haven't checked with Google, but I believe the "number two's" are more common. Perhaps for that reason I prefer the "number one's."

To me, the "like" version is stronger, and more poetic. You make a positive statement right up front, and then reinforce it with a comparison.

With the "as" version, you have to wait to find out how rough the hands are. (Maybe not as rough as you thought.)

The "like" version has a sense of two statements with a slight pause between. I think a comma may be optional. The "as" version charges ahead.

Sometimes in casual usage the first "as" is omitted: "Her hands are rough as a peasant's."

"As" may be substituted for "like" in the first version, but I'd say a comma would usually be used: " - - - our voices - - - are quiet and meaningless, as wind through dried grass - - - "
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Avangi, thank you very much for your detailed and clear answer.

In my language #1’s and #2’s would be translated the same. That’s why I can’t feel the difference between them. Now as I understood the sentences with “like” sound stronger and more emphatic. And the sentences with "as..as" sound more neutral.
Alex+ the sentences with “like” sound stronger and more emphatic. And the sentences with "as..as" sound more neutral.
Yes. I feel positively about it. Others may disagree.

Of course a strong or a weak comparison may be made using either version, if we're talking about the image itself. Perhaps what I mean is that the "like" version "grabs" the reader more strongly.