Either one would do, moss does better in shade then thyme but it can take shade as well, but does better in full sun.

Here is a link that might be useful: Propagating Perennials

Thanks for your input and for the link. Marty

Irish moss, Sagina subulata, is not a moss at all - it just looks moss-like :-) And it prefers full sun and rich, moist soils. Personally, I don't think either are good choices for mostly shady areas. For partial shade areas, I'd consider Corsican sandwort (Arenaria balerica), Corsican mint (Mentha requienii), blue star creeper (Pratia/Isotoma), or baby tears (Soleirolia soleirolii).

I have tried both Irish and Scotch moss in partial sun and it doesn't do well at all. As advised, it isn't really moss and it needs full sun.