"Compared with" is used to evaluate two things that are "side by side" ("Company A's stock price fell 12% compared with Company B's stock, which fell only 7%"). "Compared to" means to show that things are similar ("He compared his car to a donkey--both of them needed a lot of fuel, but didn't go very fast"). In your sentence, "compared with" is correct ("The fifty percentage increment of Americans coming to Thailand when compared with the previous year is noticeable"). Note the other changes I made in the grammar.

There is no difference. You can use either. You did make one mistake though. 'The fifty percentage increment of Americans coming to Thailand when compare to/with THE previous year is noticed'

Both "compare" and "compared" are verbs, but "compared" is either the simple past tense or the -past participle form. In your example, you're using "when" before the verb, so then we use the past participle form. For example, "People when seen from an airplane look very small." Here the verb is "see," the simple past is "saw" and the past participle is "seen." Because we have "when," we use the "seen" form of the verb.

Hmm, may be it's a difference between an American- and English- English, isn't it?

Thank you Brad C and Eliot. Though, I got confused which one is correct.