I am propagating both pachysandra and spotted dead-nettle (I'm pretty sure the variety is Chequers) from cuttings to replace the mulch beds in my backyard. I am in Ohio, US.
Will the pachysandra choke out the spotted dead-nettle?
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Pachysandra is, IMO, far more vigorous than any of the deadnettles (AKA Lamium spp.), so given that it is nearly the same height or even a little taller than Chequers, it should relatively easily out-compete it. This assumes, however, that your site contains little to no direct sun; pachysandra does not do nearly as well in sun as lamium.
Note that my answer is anecdotal and not based on scientific or trade-developed information, as I couldn't find any, so it could be worth only what you've paid for it :)
Frankly, if I had to choose between these two I'd choose Chequers. Where I live, the evergreen property of pachysandra is worthless in the winter because it's usually covered in snow anyway. If I had to pick anything as a shade-loving groundcover, I'd choose neither - I far prefer Epimediums, especially 'Amber Queen', over anything else. I should also note that Amber Queen is, like pachysandra, evergreen.