1. You will get a lot more flexibility to fully correct your geometry with a digital service menu, but I would not recommend trying to adjust it with the remote every time you switch games, (although you might be able to get horizontal position control by simple running the c sync line you're plugging into the TV through a pot). Use a test pattern to set it to a happy medium which will be a good compromise for all the console games you play. If you use a PC with it, you can adjust individual resolutions at the PC end. Also, with any digital chassis CRT you should make sure it can in fact display 240p without upscaling, meaning do you see real scanlines?
2. With the analog adjustment pots, they could be removed and the connection points wired to external pots with nice adjustment knobs. This would make it feasible to adjust more often, but the amount of adjustments possible could be more limited. Overall size and position will be simple, but what about straight geometry in particular areas, especially at the corners, and vertical linearity and s-correction. Get a cross-hatch pattern up to see what's really going on. There are maybe two dozen important geometry adjustments in a Sony digital service menu, and I doubt there will be that many adjustable pots.
Trying getting them both adjusted as best as possible (using test patterns is very important), then compare to see which looks best to you. Look for color, clarity, and scanline thickness in-game, and look for geometric straightness and convergence with a test pattern. For vertical linearity and s-correction, play a vertically scrolling game, and watch if things scroll smoothly, or if the getting bigger and smaller at different areas of the screen, appearing to warp or distort as they move up and down.
The last thing is whether these TV's are round or flat-faced tubes. Flat face tubes are nice, and much easier to make a bezel for, but flat Sony CRT's usually have slight a horizontal bowing that can be impossible to totally get rid of without making complex physical adjustments inside with the deflection yoke and other magnets.