How important is a Linear Power Supply Versus a Switcyed one?

I don't know.  Perhaps SMPS is in standard production while LPS is not (requires modifications).

Not very if both are done well.

Mapman - what are you saying as to why the LPS is an optional extra cost item?

Sorry didn’t read your entire post.
In your case sounds like the maker is saying the linear supply is better for this specific unit. Lower noise level I would expect. Low level Phono preamps do not require a lot of power but are most sensitive to noise. I would expect there would be specs that indicate noise levels in both cases for an upgrade of significant cost. Independent bench tests would be even better. A money back guarantee on the upgrade would also be nice. Or you can just trust them if they are a reputable vendor. Lower noise levels do typically result in better sound. More detail, better soundstage and better imaging.  

At almost any power level, a switch mode power supply will be cheaper than a linear power supply, not to mention more efficient and hence cooler. if standby power is important, they can also superior for that  (think always on waiting for a remote). Of course, they are also smaller if not much much smaller for the same amount of power.

Noise comes down to architecture and of course making the design trade-offs for low noise, which usually means giving up efficiency and increasing cost. A switch mode supply may create more high frequency noise on the AC line, but it can also create far fewer high current harmonics on the AC line at audio frequencies and have much better power factor and much lower THD on the AC input.