Do I stick with the standard Shimano DX which I’ve used on and off for years or try the Sturmey Archer one which is at least half the price of the Shimano one?

Neither!
If your looking at the ‘budget’ end of the market (i.e. Not White industries!) then I’d go for an ACS Crossfire.
Look at Triton Cycles, they have them for about £16.
Far better than either the DX or the Sturmey Archer, and I’ve tried them all 😉

I got a good deal on a 1/8″ Token – nice shiny finish and serviceable, also makes a nice zzzzzzzzzzzzzzzzzzzzzz for just over half the price of the White Industries.

Sturmey Archer are heeeeeeaavy

I doubt I’ll notice the weight penalty – it’s for my commuter – a Pompino with mudguards and marathon plus tyres.