It’s all a matter of perception and personal physical endurance . . . typically the difference is as basic as girl vs. boy . . . I’m talking about not feeling well. Where a woman will be feeling a little peaked and under the weather, a man will be non-functional and sick as a dog.
‘Sick as a dog’ . . . an interesting phrase. I don’t think I’ve ever heard anyone say “I’m as sick as a goldfish”. Of course, I’ve never seen a sick goldfish before . . . they’re usually either alive or dead . . . I guess if someone was as sick as a goldfish they’d be in a dire condition indeed!
Anyhoo . . . the phrase originates across the pond in merry ol’ England where being sick isn’t merely having a sniffle or the flu. Being sick in Britain usually means barfing.
What animals have you ever seen puking? Cats and dogs mostly. Horses can’t vomit, by the way . . . and cows just do it in their mouth and keep on chewing.

To fully appreciate the original sense of "sick as a dog," picture this . . . while basking in the after glow of a lovely meal and enjoying a delightful glass of wine in front of a romantic fire with a beautiful woman (or man or whatever you prefer) when Max lurches into the room after consuming a banquet from the neighbor’s garbage can and displays his gastronomical discomfort all over the floor at your feet. Aaah . . . what a lovely portrait I paint.
So, if you’re sick as a dog it’s supposed to mean that you’re ill enough to be up-chucking a lung . . . at least if you’re a girl.