Everybody has opinions and many are very adamant in their declarations in favour of one machine or another. My observations:
I have used and worked on American, Canadian, English, Japanese, Taiwanese, and Chinese machines. The impression I have gotten is that the Taiwanese machines were a copy of American and European machinery and the copy was made from a blurred photograph. The Chinese machines were copied from a similarily blurred photo of the Taiwanese machine!
I don't think it is possible to buy any kind of manual lathe from Japan any more and manual American lathes are also rare. Standard Modern (Canadian!) still makes manual machines which are spendy but very nice.
The truth is that Taiwanese machines work just fine. I use a 13x40 Advance which I've had since 1986. It's been quite satisfactory.
In a busy machine shop I worked in, we used two old Mazak lathes (Japanese). These were big spindle bore (3 1/8 inches as I recall) machines and worked steadily without a hitch under very rough conditions. I replaced all the bearings in the headstocks of both but more because the owner felt it should be done than out of necessity. Later, he bought a lathe from Modern Tool (Called a "Modern". Don't confuse this with Standard-Modern!). This lathe was a copy of the Mazak (blurred photo!). When new it performed very well with a couple of minor glitches and continued to perform well for about 5 years. At this time a rebuild of the headstock was necessary to replace some worn bearings. Keep in mind, these machines were used under very harsh conditions. Cutting apart big hydraulic cylinders and rods is hard on a machine. In the end, the Chinese machine was fine for the purpose. It cost about what one would have paid for a decent used Mazak and worked as well but not for as long without some extra maintenance. Since it is about all that was available of the type, it wasn't like one had a lot of choices.
In the same shop, there was a 13x40 Advance geared head lathe which the owner had bought used. This poor thing was thrashed mercilessly and was used as a polishing platform as much as anything. It's been in constant use in that shop for at least 15 years now and still works amazingly well.
In the end, the Amercan machines are nice and well made but are a bit quirky (just like an older Harley!) The same is true of the British machines. Really, the machine may be less important than how it is used and maintained. Spend what you can afford and learn to do what it can. Regards, Bill.