What is a more effective shield for magnetic fields between 300 and 500kHz Solid copper or copper mesh?
My only worry is the high frequency AC magnetic fields


It's really all about a thing called skin depth: -



Graph taken from this wiki page

So, for example, at 100 kHz, copper has a skin depth of about 0.2 mm and this means a 1mm thick screen forms a fairly effective shield against magnetic fields leaking out or leaking in.

I don't think that (even) 2 oz copper on a PCB is going to be that good whether solid or hatched. 2 oz copper is about 0.07mm thick so maybe you will get a little attenuation.

At 300 kHz it's in that borderline area where you might get a reduction of a couple of dB but if you are expecting a few tens of dB then it's very unlikely. 

At 500 kHz (where the skin depth is about 0.09 dB) you might see a 5 dB reduction. Having said that, every dB counts so it might just be enough.