I believe that convention flat square CRT technology still has many advantages over flat-faced CRT's. Price being the most obvious. From what I have seen, the only real benefit of flat-faced monitors is some glare reduction. For me I can control glare in a number of ways. Remove light bulbs, change the position of my desk, close a window shade etc. Saving $$$ is more important to me. Another option is to purchase an after market anti-glare screen. This acts basically the same as a flat faced CRT and may save you $$ in the long run.
In general conventional CRT's tend to give sharper characters for a few reasons. They tend to have a tighter horizontal dot pitch 0.22mm, better convergence specifications and the fact that the tube is curved in two directions makes it easier to adjust focus uniformity and convergence at the factory. This is not to say every conventional monitor will provide better text, these attributes simply increase the odds of getting better text. Monitors vary model to model and lot to lot it is important to check the manufacturer specs.
The ability to display fine detail on a computer monitor involves many factors including resolution, dot pitch, spot size/shape and convergence. Convergence is one of the most important aspects of a monitor's performance. It determines how sharp the characters in your text document or spreadsheet look. Convergence has a direct effect on the monitor's apparent focus. Unfortunately, convergence is a spec that few manufacturers publish. To my knowledge none of the flat CRT brands publish convergence specs.
There is a reason that the original televisions had almost round picture tubes and that today the IMAX theaters use a domed screen. In general it is easier keep focus consistent if you project a beam onto the inside of a curved surface. Almost every monitor has better focus in the center of the screen than at the edges. This is because the beam is at right angles to the screen. The trick is to keep focus uniformly good over the entire screen.
Try this experiment. Take a flashlight and aim it straight at a wall you will see the spot the beam creates is sharp and round. Now aim the flashlight up into the corner of the wall. You will see the beam shape change to a more oval shape and spread out. In general terms this is what's happening in your CRT monitor. The flatter the surface the more the beam spreads out or defocuses. Now imagine that you are in an IMAX domed theater. If you shine the flashlight at any portion of the inside of the dome, the beam shape and size stays much more consistently focused.
Yes manufacturers have developed technology (dynamic focus circuits, etc.) that does a good job at improving beam shape and size in the corners of the screen. However no circuit or technique can make the beam 100% accurate. Again on average and because of these facts, I believe that conventional shadow mask monitors with slightly curved screens will produce a better more consistent image.