It depends....
The real difference between a single and a double wall skin is that when the fly gets wet on the underside, from condensation, with a double wall you rub against the inner wall and hopefully that is still dry, if you do that in the single skin tent you rub against the wet wall.
In really bad conditions, that condensation can drip on you.
If inside a single skin tent you could wipe that off ( I use a kitchen cloth) or just moan about it, inside a double wall the inner may absorb/repel those drips but sometime they do come through particularly with a mesh inner.
When the inner drips on you there is not much you can do if you can't un-clip it from under the fly (integral pitch tents allow you to do that)
I have, on several occasions, walked out of a single skin tent warm and dry only to find folk in nearby double skin tents complaining they had a cold night.
Yes cold from being all zipped up producing a lot of condensation that gets trapped inside the fully sealed tent.
BTW, I am in Australia but contrary to popular belief it does rain here too (just not at home right now that we need it) and getting up with everything around wet after a non rainy night is not all that unusual.
oh, and we get snow too...