Once and for all I'd like to know if it's generally better (factory recommended?) to change automatic transmission fluid the traditional way or have it flushed?

The factory-recommended way is to drop and clean the pan, replace the filter, and refill with the proper transmission fluid. Normally, this changes about half the fluid in the system, leaving the old fluid in the torque converter, transmission cooler, and lines. After you perform the factory-recommended approach, it's preferable to read how to take the next step and change all of the old fluid.

The problem with most commercial flushing machines (e.g. T-Tech) is not the machines, but the fact that the pan is not dropped and cleaned and the filter is not changed. Therefore, there's a high probability that the T-Tech machine will stir up all of the crud on the bottom of the pan, clog the filter, and result in transmission failure.

After dropping and cleaning the pan the first time, I install a B&M Transmission Drain Plug. It makes subsequent changes a snap. I also recommend using full-synthetic ATF when you can. It makes a huge difference in how ATXs perform, particularly in cold weather; how long they last; and improves gas mileage.