The deeper the better especially if it rocky soil, water will not be retained so go with 4" and you will not have to water as much.

Actually, the thyme will do very well in your existing "cruddy", sandy/rocky soil, providing that soil drains well. Thymes and other herbs with Mediterranean origins (lavender, rosemary, oregano, etc) are low water or xeric plants native to areas that tend to have very lean, rocky soils with excellent drainage and prefer those kind of conditions over soils that are overly fertile and moisture retentive.

Personally, I'd save the better soil for areas that are going to accommodate plants with deeper roots and fussier preferences :-)

Thanks to both. I did a little more googling and found exactly your point, gardengal, that thyme wants drainage. So it's getting two inches of soil, the "proper" flower bed is getting extra soil, and my back and shoulders are a bit grateful that I didn't have to pick/shovel as deep this morning.