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On the Mac I use ImageAlpha to reduce the colours to 256 (it has a preview window so you can see if it's OK), then when saving the file I choose the option to send it to ImageOptim.

On Linux you can get the same by using pngquant, then using trimage. AFAIK there's no GUI frontend for pngquant so I guess how many colours would be ok and check before running trimage.

The reason why I use 2 tools is that ImageAlpha/pngquant is lossy and ImageOptim/trimage is lossless.

I think ImageOptim uses the pngcrush library.

This website looks neat, but it seems like a CLI that can become part of my automated workflow would generally be more useful.

The tools you mention use lossless compression. For 24-bit PNG files that means they probably won't come close the kind of lossy compression used by TinyPNG.

The comparison will be subjective. One will retain full detail (24-bit color) and the other will not. The "better" will be subjective, as I said.

I wish Photoshop gave the option to save an 8-bit PNG with a FULL alpha channel—that's what this seems to do.