Now, Korean and Japanese have been proposed to be part of other language families, for instance Altaic, but Altaic is not considered a valid term subterfuged by evidence as much as Sino-Tibetan and Indo-European. However, often both are described as isolated languages.
I know some very simple Japanese and Korean, and for a layman I see the similarities in grammar like:
agglutinative building principle
no strict difference between what we would consider adjectives and Verbs, both can act as Predicatives
The Predicate is in the final position, all other phrases come before it in no fixed order followed by a particle that tells the semantic role in the sentence.
Verbs and Adjectives are being marked for social relationship between speakers such as politeness, respect, humbleness.
Than, both sound related, though I hardly can find cognate words that sound similar, for instance:
the words for ugly are minikui and mossaengi in Japanese and Korean respectively.
na and watakushi for I
dal and tsuki for moon
At least the words for bear sound similar (the Korean mythology tells about a bear princess and some guy who fathered the Korean people, The Ainu in Japan have strong mythological meaning for bears also)
- kuma in Japanese and kum in Korean
Another feature that sets them apart is Korean sandhi rules are very elaborated while Japanese neglectable.
Could you name further features that are considered as pro or contra arguments for a common origin ?