Arabic and Hebrew are Central Semitic languages with many similarities in vocabulary and structure. But how similar are the gender of their nouns? I know they both have masculine and feminine nouns, but what is the level of correspondence between genders in these two languages? Do the same words use the same genders? This would be useful to know for a learner of these languages.
Yes, definitely a positive correlation there!
Names of body parts that come in pairs are usually feminine in both languages.
Names of cities and countries are usually feminine in both languages. Likewise the word for "land" — קרקע/أرض.
A small grab-bag of miscellaneous words are feminine in both languages: fire, cup, well, sun... There are some 25 such "cryptofeminine" nouns in Hebrew. If you're serious, you might as well just memorize them all.
Fortunately for you, gender is usually obvious from the final letter — ة, ה, ת as the case may be (though in Hebrew beware of roots that end in ה or ת).