In that scale, is there any difference in the shade of grey for hull/superstructure and tan(?) for the deck between one nationality and the other?
Yes, but the small surface area means you have to use pretty markedly different colors to see any difference.
I can't offer cogent advice on Vallejo colors, but I do have general advice about painting 1/6000 ships:
I found with grays that the main noticeable difference was in shade – dark, medium, light. I tried adding some bluish hue to my Austro-Hungarian fleet and can barely tell unless I'm specifically looking for it. The surrounding blue sea surface overwhelms the blue tint and they just look gray.
Deck colors actually can make a big difference, because the light reflecting off of horizontal surfaces is typically much more noticeable (and probably greater) than the light reflecting off vertical surfaces (unless you're using a table-level light source). I found that differing deck colors was the easiest way to distinguish nationalities between gray opponents. As with all things 1/6000, you'll have to choose colors that are more severely different from each other and quite a bit brighter in the jar than you'd like, but if you stick to broad categories like pale, yellowish, light tan, dark tan, and reddish (e.g. Japanese linoleum)
I never found a wash much use at this scale. Except maybe on battleships, the details are really just too small to hold enough liquid.
Drybrushing works brilliantly, but you have to use pretty high contrasts between layers. Also keep in mind that the tiny scale means you need to choose a color much lighter than you'd expect to get the final impression you want. I wanted my WWI Italians to be a pretty light gray, and I ended up painting the vertical surfaces with a pretty light gray and drybrushing with a near-white to get that. DDs, TBDs and torpedo boats that are supposed to be black I actually paint a dark gray and drybrushed lightly with medium gray, and even that is too dark to see.
Finally, I recommend painting the US ships in the various non-gray cammo schemes if you can get away with it. They're not too hard to do at this scale, they make the ships more easily identifiable, and colorful dazzle cammo schemes are really nice eye candy on the table.
- Ix