Craig Cartmell is a regular on TWW - you could ask him there what 'improvements' have been made.
I've never seen a copy so couldn't tell you what the rule differences are.
The price difference is probably because they ducked from under the Osprey cover (and formatting restrictions). The new edition is an independent printing - hardback, apparently with better structuring and not so closely tied to North Star figure ranges.
As for prices - the old Osprey version seems to selling for insane prices on Amazon - £40!? whereas I found a new version of 2nd ed for £30. https://www.snmstuff.co.uk/product/in-her-majestys-name-second-edition-hardback-edition/
No idea who they are or how reliable (and probably insane postage to Oz). But prices seem - variable.