"The dress is as white as snow."
Translation:Mekko on valkoinen kuin lumi.
How would you describe the difference?
Yhtä kuin of course allows for precision in comparisons, but only when the comparison hits something countable, which yhtä generally would refer to.
"Märkää kuin vesi" or "Yhtä märkää kuin vesi" doesn't seem to have any difference in meaning, since an adjectives scope mainly changes through comparative: "Märempää kuin vesi", but then you can't use "yhtä" anymore.
On the other hand "yhtä iso kuin Venäjä" or "iso kuin Venäjä" are of course completely different in meaning. The size of Russia is absolute (at least by some definition at a certain point in time).
In written form I think using conjuctions are better avoided. With or without "yhtä". If not necessary for rhythm, clarity or accenting something, of course - they do have their purpose.
"Mekko on valkoinen kuin lumi." "Mekko on yhtä valkoinen kuin lumi." "Mekko on lumenvalkoinen/lumivalkoinen."
It seems these all would share the translation "The dress is as white as snow." as the most natural expression in English. The most fluent expression would be that without conjuction, since it's not necessary in a sentence this short.