By galleys and junks I just mean ships/water-going vessels of each of their respective cultures. Also, by a comparison I mean what are the strengths and weaknesses of both ship styles and where and how does one have the advantage over the other such as; speed, mobility, armorment, battle worthiness etc. Please note that I'm asking for a comparison, not necessarily who was the absolute best at seafaring/ship building.
I don't think enough materials on East Asian civilizations from that era survived to make a detailed comparison, so what I can make are, at best, educated guesses based on what I know.
(By the way, early East Asian warships were completely different from what we today will recognize as "junk". Junks are sailing ships, whereas early East Asian ships were oared.)
From what I can tell, at least in China during the Han Dynasty (Korea was still in its Gojoseon era, and I know next to nothing about them), and its preceding Qin Dynasty and Warring States, focused more on riverine warfare. This means their ships would be more optimized for that kind of warfare, but how this translates to other qualities like say "seaworthiness", I can't tell.
As far as tactics and technology go, East Asia warships seem to lean heavily towards the shooty side, as opposed to the classical galley with its ram and boarding (they still did not shy from boarding action though). The Chinese capital ship of the era, known as "Louchuan" or tower ship, is essentially a big, three (or more) decked floating fortress. The early mass-adoption of crossbow and traction trebuchet (single pole trebuchet takes up very little space, so you can mount a literal boatload onto one ship. Also it can pivot to shoot at another direction, and doesn't have tremendous kickback like torsion-based siege engine that may damage the deck) probably helped them in this regard.
Chinese warships seem to be enclosed rather than open-top, and its uppermost deck often had crenellations.
Common Han-era warship classes were: Louchuan (Tower ship/capital ship/flagship), Doujian (Fighting ship/general warship), Mengchong & several other classes of "assault" ship like Maotu, Lunao, Xiandeng, Chimazhou etc. (their difference and roles are unknown, but seem to be distinct ship classes. Probably include some kind of general purpose light warship, dedicated boarder, and at least one type of heavily armored fast attack ship designed to dash into enemy formation and shoot at every direction), and Chihou (scout ship) etc.
As a side note, Chinese people also invented sternpost-mounted rudder at around 1AD, although they still used steering oar. What benefits this invention bestowed to their warships, I have no idea.