If you mean "than Korea presently is," then there is at least one significant difference to consider in determining the level of comparison. During Japan's period(s) of hermit-like policy, the restrictive policy was intended to keep foreign influence out of the country. Otherwise, Japan went on fairly much as it always had done. Korea in the present era may perhaps be viewed differently. Korea is not only protective, it is also antagonistic. Korea not only withdraws into itself, it fosters a milieu of antagonism.
Interestingly, David Mitchell's recent book, The Thousand Autumns of Jacob de Zoet, deals precisely with this issue as it depicts a Japan that is just opening up its borders to foreigners and the trade that they bring, though very reluctantly. I have to agree with #3 more than #2. I do think that Japan was more strict in terms of isolating itself from foreign influences and as a result was more of a hermit nation, though at the same time I do think Korea was a hermit nation to a lesser extent.
The period in which Japan was a "hermit kingdom" was not after 1863, it was before that period. This is the period known in Japanese history as the "Sakoku" period. Sakoku was instituted in the 1630s and lasted until the "opening" of Japan by the Americans in the 1850s. During that time, no foreigners were allowed in Japan (except at one trading facility that was on an island in Nagasaki harbor) and no Japanese were allowed to leave. This was a much more complete sealing off of the country (though some Western learning was allowed in to the country via the Dejima trading outpost) than was possible in Korea.
I would argue, then, that it is more correct to call Japan of the Sakoku period a "hermit kingdom" than it is to use that term to describe Korea.
The term, "hermit kingdom" is used to describe a country that directly shuns foreign involvement. It can describe many different countries. However, it has come to describe Korea on account of a book by William E. Griffis' book, entitled Corea: The Hermit Nation, which was published in 1882. The book was unfair as Griffis had never visited Korea or even had any experience with Korea. Moreover, there was an agenda, namely to prove that the Japanese were superior to Koreans.
In 1863 the emperor of Japan issued a decree expelling all foreigners from Japan, which resulted in minor conflicts. But this movement did not gain much traction.
In light of these two points, two conclusions can be made.
First, it is unfair to call Korea a hermit kingdom, since this term applies to many countries much more than Korea, even if it is true that Korea had little involvement with the rest of the world.
Second, since the edit which sought the expulsion of foreigners did not gain traction in Japan, Japan did not become as insular as people think. As to the question of comparison with Korea, it is close. The jury is out on this one. For example, Korea embraced Christianity, which was foreign. Japan did not. This has made a very lasting difference. In light of this, I would say that in some ways Japan was more of a "hermit" nation than Korea.