Most people probably have really limited experiences, especially comparing such schools in different parts of Taiwan.
I can only comment on my own situation. I’ve worked/work in a junior high school in Taoyuan, although we actually do the majority of our work with elementary school kids. This is my sole experience in the public system (and I previously worked for a major chain buxiban and its kindergarten).
I suspect the bad points are fairly systemic/culturally uniform across Taiwan, or maybe they’re the result of certain individuals. Either way, I don’t know that there’s necessarily anything that can really be said about them that lots of other people haven’t already discussed when discussing this country and culture in general.
In the main, I really like my job. I get a much higher level of respect (since I’m considered a teacher, not the singing clown throwing the sticky-ball like I would be at a buxiban) and freedom in teaching decisions than I ever did working for a buxiban.
Furthermore, the benefits are better. Paid holidays (although I don’t get as many as most, but they’re still paid). Good pay that is tax free. Spin offs like privates and big money hosting local government speech contests, etc. that a buxiban would obviously not pass onto you. Also, a fairly low-stress work environment. I teach about three hours per day. The rest of the time is my own. Even taking out time for planning, I still have plenty of time to spend online, in the school gym, reading, even sleeping. You really can’t go wrong as a real teacher compared to being the clown in the buxiban.
Dunno, sorry I can’t offer more of a comparison than that. Like I said though, I quite like my job and I suspect public school jobs would generally be the best option here.