Size looks to be the same, or nearly so. With some digging you might find numbers to confirm. It can't be far from the Uno footprint though.
And, my god, $40 for an Uno clone? Really?! $15 is a heavy price to pay for a few prototyping holes, a better silk screen, and a real crystal on the chip.
A quick googling shows that Arduino Uno cases are abundantly available online.
That said, getting good cases that work well for what you're doing is always a challenge, because everyone wants a slightly different case. You want to fit the 16x2 character LCD on, but I want to fit a 3.1" COG 128x64 LCD, and someone else wants to use a colored TFT display. You need vent holes because you have a shield that gets hot, but the other guy wants to use it outside in the rain, so he needs it sealed. The arduino uno cases I saw on that quick google certainly don't give you much room for connected electronics.
Of course, if you have a 3d printer and know how to use it, you can make whatever shape case you want; I think this is what all the cool kids do.
Last time I needed a case, I grabbed a plastic bin off the shelf, dumped the crap out of it, cut some holes in it, and stuck my electronics inside, with scotch tape over exposed pins to prevent shorts.