I have occasionally pondered the similarities and differences between these two cities (shown above as close as I can to the same scale). I think there are more differences than similarities. Both are the biggest city in their country, but Seoul comprehensively so and Sydney only just (and is projected to be overtaken by Melbourne sooner rather than later). Seoul is the capital of South Korea, but Sydney isn’t the capital of Australia, even though many people around the world think or assume it is. As a result, Sydney (and/or Melbourne) dominate economically and culturally, but not politically (at least at the national level; they dominate their respective states).
Geographically, both sit between the ocean and mountains. Even though South Korea is overall more mountainous, Wentworth Falls (at the far left of the Sydney map) is higher in elevation than Bukhansan. It’s just that Bukhansan is located comparatively much closer to its city. (Also, Mount Kosciuszko (the highest mountain on mainland Australia) is higher than Hallasan, and Mawson Peak (the highest on an outlying territory) is (just) higher than Mount Baekdu.) Both are at similar latitudes (Seoul 37ºN and Sydney 33ºS), but Seoul’s weather is dominated by the Siberian high and East Asian monsoon, meaning very cold winters (with snow) and very wet summers (with occasional typhoons) while Sydney’s is more equable, very rarely getting super-cold or super-hot (at least towards the coast; my inland suburb is more variable, and one day a few years ago a suburb near here was the hottest place on the planet).
Politically, there is an entity named 서울특별시 (seo-ul teuk-byeol-shi, Seoul Special City), which is the area surrounded by the red line on the map. There is no equivalent entity in Sydney. The equivalent area is divided between all or parts of 34 cities, municipalities, councils and shires, roughly equating to Seoul’s 25 구 (gu, districts). The City of Sydney is just one of those, and a very small one at that. It roughly equates to Seoul’s Jongno-gu. The area surrounded by the red line on the map seems to have no official definition. The closest thing to any official definition of Greater Sydney is the Australian Bureau of Statistics’ Greater Capital City Statistical Areas, which is a “geographical area … designed to represent the functional extent” of the city, but the ABS notes that it “extends well beyond the built up edge of the city”. I can’t find any official definition or map of that area. The next largest political unit is New South Wales, which is several times larger than the whole of South Korea.
In terms of population, Seoul has approximately 9.75 million people and Sydney 5.3. (In fact Seoul has only slightly fewer people than Sydney and Melbourne combined.) But that’s just Seoul Special City. The Seoul Capital Area (수도권, su-do-gwan), Seoul, Incheon and Gyeonggi-do combined, has approximately 26 million people, approximately as many as the whole of Australia. Most of those live in the area shown on the map above, but there are cities, such as Suwon (1.2 m), which lie off the map. Clearly, not all of Gyeonggi-do can be classed as ‘part of Seoul’. Perhaps the simplest working definition is call the cities of Gyeonggi-do which border Seoul ‘part of Seoul’ and those that don’t ‘not part of Seoul’. It’s hard to say that Bucheon and Gwangmyeong aren’t ‘part of Seoul’. When I lived in Goyang, I told my family and friends that I lived ‘near Seoul’, not ‘in Seoul’. On the other hand, the nearest population centres to Sydney are the Central Coast (350,000), which is really a collection of separate towns, and Wollongong (295,000), which despite its smaller population (which I am surprised to learn) is more a city. (Seoul and Gaeseong are closer than Sydney and the Central Coast or Wollongong!)
Seoul lies within a short plane ride from Shanghai, Beijing and Tokyo, all of equivalent size. Sydney and Melbourne have no cities of equivalent or greater size between Johannesburg, Jakarta and Santiago (mostly because most of what lies between is ocean). Sydney and São Paolo are the only two GaWC Alpha cities in the southern, while Johannesburg, Melbourne, Santiago and Buenos Aries (and Seoul) are Alpha -. On the other hand, Melbourne loudly proclaims any list of liveable cities which places it above Sydney. (The lists on this Wikipedia page rank Melbourne higher on three lists, Sydney on two and Adelaide on one. But they are measuring (or attempting to) different things.)
I actually lived in Daejeon (1.5 m) and Goyang (1 m) and have only ever visited Seoul, but Seoul is a more apposite comparison to Sydney.
^ to answer Moonfriend’s question below about whether the Central Coast (which is counted in Sydney’s population statistics) is contiguous with the Sydney metropolitan area. All the dark green is dense bushland.