You didn't set a definite range for the scenario to work, so I'm going to present quite a few scenarios.
Around 100-650 AD, Korea was divided into three (technically four) kingdoms, which were Goguryeo, Baekje, Silla, and Gaya (which was not considered a kingdom for several centuries). Goguryeo controlled about 1/4-1/2 of Manchuria and the northern Korean Peninsula, while the other three kingdoms occupied the southern Korean Peninsula. Although Japan was not as stable an entity as those Korean kingdoms, they still had a very loose form of government, and had emperors/kings.
Goguryeo or Baekje could have easily conquered Japan if they had seen the need for it, but because Japan was a collection of islands that were significantly far off from Korea, they decided not to bother, and Baekje actually ended up allying with Japan for a significant period of time, and when Baekje fell to the Silla-Tang alliance, there was a brief attempt at restoring the kingdom, which was led by a combination of Baekje and Silla troops. However, they failed, and Silla ended up uniting the peninsula at around 660-668, although Balhae was founded after Goguryeo's downfall, and Silla never technically unified the peninsula, because Balhae still retained all of Goguryeo's territories, and actually expanded into what we now consider Russia's Far East.
If Gwanggaeto the Great, who greatly expanded Goguryeo's territory, had united the peninsula at around 400, but not invade Japan, then Korea might have managed to remain united until about 1000-1400, and theoretically, Japan would never have managed to attempt to invade Korea, meaning that Japan potentially could have been much weaker and Korea would have been much stronger than in OTL.
Because we're not interested in whether Korea would have been able to subjugate Japan, let's fast forward to the late 1500's, considering that every other event before that preceeded as in OTL. During that time, Korea was very weak in terms of the military (at the beginning of the Imjin War, Korea had only about 84,000 soldiers) because they did not have a consolidated army. Japan, on the other hand, had recently been unified under Toyotomy Hideyoshi, so they had a massive army (numbering about a million, give or take) and a reasonably strong navy. Japan could have easily overrun the entire peninsula and made Korea into a colony, judging from the almost complete annhilation of the Korean army and a de facto Japanese rule of the Korean peninsula (not to mention the thousands of ears that Japan brought to their temple to prove how many Korean soldiers they captured) and even possibly invade China to bring a significant portion of it under Japan's control. However, Yi Sun-shin, who had a very unprepared and undermanned army, managed to repel the Japanese army by utilizing the geography and his superior tactics, which effectively crippled the Japanese on land. In fact, in the Battle of Myeongnyang, the Korean navy numbered barely 13 ships, while the Japanese navy possessed 333 ships altogether. Yi Sun-shin, however, managed to all but destroy the Japanese fleet by effectively disabling about 100 ships, while losing no ships and having only 5 casulties on his side. In other words, Yi Sun-shin was the only person that basically prevented Japan from winning both wars (Hideyoshi led two invasions).
However, this does not take into consideration the situation that had been developing before the war, and that almost no one even bothers to consider. Yi I, a prominent Confucian scholar who lived from 1536-84, advised King Seonjo to raise about 100,000 Korean troops, stationed all over the Korean peninsula, in preparation for a Japanese invasion. Because the king was incompetent and only listened to his more "trusted" advisors, he ignored his plea, and the scholar soon died only eight years before the Japanese invasion. Had the king realized the dire situation that Korea was in at the time, then Korea would have ended up preparing about 100,000-500,000 troops, and although the army would still have been outnumbered, they would still have been able to effectively repel the Japanese invasion, because the navy wasn't much of a problem.
Now that we know how Korea might have prevented the Imjin War, which Japan would not have been able to win unless Yi Sun-shin was either executed, which came extremely close to becoming a reality in OTL, or even killed during (not right after, as in OTL) the war, it's pretty reasonable to assume that with a few other tweaks, Korea and Japan would have remained equal until today. This would be achieved if Yi Sun-shin had not died at the conclusion of the Imjin War, or the Heungseon Daewongun, or any other member of the royal family, had decided to modernize more quickly than in OTL. Either or both of these scenarios would have led to a much more militarized and westernized Korea, and they would have been able to revoke or not even sign the unequal treaties that were forced upon them by Japan.
All this is very quickly worded out, but if you take all of these into consideration, then Korea and Japan might have been considered as equal, rather than Japan as "superior." Of course, all this means that WWI and WWII would have turned out to be very different, but that's another story.
I hope all of this extrapolation helps.