Those summaries you linked about Taiwan are Winston's opinions and personal perception based on his own experiences, extended family views, and some conversations he's had with certain others who generally agree with his bias.
But a lot more has been posted on this topic in the last couple of years. I've debated with Winston at length on the merits of Taiwan as an attractive 'Happier Abroad' destination and even met with him to approach and connect with various Taiwanese strangers. I stand by everything I've written so please do a detailed search on Taiwan related posts if you want to get more balanced view of this country.
As for your specific comparison request, I'm not in a strong position to say too much. While I've lived in Taipei for quite awhile, I only have limited experience with Korea and Koreans and even less with Japan and the Japanese. Here are a few off-the-cuff thoughts though:
If we focus on the capitals (Taipei, Seoul, Tokyo):
- Taipei is by far the smallest - population 2.6 mn vs. 13 mn for Tokyo and 10 mn for Seoul.
- It is easier to manage with just English in Taipei than in Seoul or Tokyo.
- Seoul has by far the fastest average internet connection speed, but both Tokyo and Taipei beat the States.
- Taipei has the most modern and integrated transportation system - MRT lines are just a decade or less old and quite extensive. Buses are mostly new and have dedicated lanes to make them faster. Taxis are abundant, modern, available 24/7 everywhere, and cheap (a bit cheaper than Seoul and much cheaper than Tokyo). With one universal stored value easy card, you can pay all for all bus, MRT, and train rides plus many of the taxis. Ride combinations get you big discounts. I've done bus + MRT rides of about 1 hour out to far suburbs for under a dollar. Automatic bicycle racks stocked with new bikes are also located in certain parts of the city. You can use your universal stored value cards to take a bike off the rack and later return it to any rack in the city. MRT passengers are even allowed to transport their bikes on-board and alight at certain stops which have designated bike trails.
- Taipei has the highest per sq. km concentration of convenience store chains (7-11, Family Mart, OK, etc.) and your universal stored value cards can be used for purchases there. Most residents have 1 or 2 of these within of block of their homes. And they fully live-up to their name - 24/7 1-stop shops for ATMs, bill payments, online movie tickets purchases, meals/drinks/beers/cigarettes/sundries, local and international mailings/deliveries/drop-offs including DHL or Fed Ex service, fax and copy service, etc. Some even have sit-down areas to eat and drink. Similar concept stores are also very common in Tokyo (from which Taipei imported much of the convenience technology and culture) and Seoul but the concentration is highest in Taipei.
- From an international or US perspective, all 3 cities are extremely safe 24/7 violent crime wise. People have small space bubbles but still very polite and hands-off (not at all in your face). In the case of Taipei, women can generally walk the streets anywhere anytime and not have to worry about being verbally harassed or approached by drunk guys (don't know if the same applies to Seoul and Tokyo).
- I believe there is a substantially higher percentage of local women open to dating westerners in Taipei than in Seoul or Tokyo and that Taipei is the least xenophobic and racist of the 3. Western foreigners often get different treatment in all 3 cities - sometimes its positive discrimination (ie in your favor) and other times its negative. I would expect that the ratio of positive/negative discrimination is higher in Taipei than the other two cities.
- Tokyo has by far has the highest cost of living. Seoul is much cheaper but still moderately more expensive than Taipei. From an international perspective, Taipei is relatively cheap (not much more than Bangkok overall for basics such as food, transport, and rent) while Tokyo is quite expensive.
- All 3 cities have very expensive real estate (global top-tier a price per sq. meter basis) but Tokyo's is probably the most pricey overall. However, rents are relatively low in Seoul and even cheaper in Taipei.
- Taipei is sub-tropical, Seoul and Tokyo have 4 distinct seasons.
- Unlike Tokyo and Seoul, Taipei has an abundance of scooters and motorcycles, around 1 for every 2 people. These are both a blessing and curse. On the plus side, they offer an extremely cheap and convenient option to get around the city. On the negative, the contribute to unnerving noise pollution with their loud and annoying 2 stroke engines.
- Seoul and Tokyo have many wonderful saunas where locals can go (often as a family) and hang-out in robes or local style garbs for hours to enjoy various hot and cold baths, steam rooms, cold rooms, suana rooms, work-out areas, restaurants, shopping, etc. Taipei's saunas are generally just for men and much lower-end, not comparable.
- All three cities have great nightlife options. And there are very cheap ways to have a fun night out in Taipei. Guys on budget (aka foreign English teachers, lol) sometimes hang-out at clubs all night but do most of their drinking at the nearby 7-11. Similar budget possibilities are probably available in Seoul and Tokyo as well but I'm not sure.
- P4P in all three cities is expensive and not user friendly. Best value for money can probably be obtained if you get plugged in with the right locals. Tokyo and Seoul are known for having many local only P4P venues though. Taipei does have massage services which advertise in the local English papers and I've read (on another website) that some of them have younger and fairly attractive girls for US$150-200 full-service ST in your room.
- All three cities are great places to buy computers and gadgets but prices for Apple items are still cheapest in States. Japan has its own hardware technology for gadgets so offers many things not available elsewhere. The cellphone and hand-held computer culture you see almost everywhere today was common in Tokyo several years earlier than in other cities through mobile operator NTT Docomo and complimentary hardware devices available only in Japan.
- Facebook is very popular in Taipei and Seoul but not Tokyo where they tend to use their own (local based) preferred social networking site.
- All 3 cities have plenty of hot and classy looking female eye candy, especially in trendy areas.
- Seoul is world famous for Asian centered cosmetic procedures (eye, dental, and orthognathic) and a substantial percentage of young local women have had subtle or not so subtle work done. This is much less common in Taipei where people are still more into looking natural. I'm not sure about Tokyo.
- As for tourism and traditional style attractions and sites, Taipei probably has the least to offer but a decent 'exotic Asian experience' can still be found here if you look for it.
- A native English speaker with a generic BA or BS degree or its equivalent should be able to find plenty of teaching work in all three cities. But the shortest and most flexible options (including non-contract) are much easier to find in Taipei. I would recommend securing such work before going to either Tokyo or Seoul. But for Taipei, you can probably come-over first and then put-together a full teaching schedule locally within a few weeks. Relative to cost of living, the pay for this type of work is probably highest in Taipei.
- I know many people who love the many Asian style food and eating options available in Taipei. I'm sure the same probably applies to Seoul and perhaps even Tokyo. It can be challenging to find western food in certain areas of all 3 cities.
- Tokyo stands-out most IMO as offering the first time western visitor a surreal and futuristic type of experience, a look into a different world - exotic urban east Asia. Visible icons of this include capsule hotels, elevator girls, suanas and spas, pachinkos, porno comic books, vending machines everywhere for everything, loudspeaker announcements, royokans, uniforms and formal business attire, cosplay cultures, yakuza, non-conformist young-set, Japanese spins on western culture, ultra high-end shopping districts, hi-tech toilets, robot technology, local style nightlife areas, etc. On the other hand, Seoul and Taipei seem somewhat more generic IMO.
That's all that comes to mind for the moment. I may add more to it or revise it later. Perhaps others, especially those with extensive experience living in Seoul and/or Tokyo can add their views.