verb
BAD : The teachers will be able to visit our schools and compare our teaching methods to their own.
GOOD : The teachers will be able to visit our schools and compare our teaching methods with their own.
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compare to = describe (someone or something) as being similar to (someone or something else); liken: 'She compared the child to a noisy monkey.'
compare with = examine two or more people/things/ideas etc to discover similarities and/or differences: 'Having compared the new dictionary with the old one, she found the new one more helpful.'