I’m 25 and learned it as catty-corner but in conversation I’d more likely say “(object/building) over there” and point, or say that it was diagonally across.
It’s cater. Yes, I was brought up to say kitty. But I’m literate, and it’s no use pretending I’m not. So cater it is. It’s from the French word quatre. ‘Four’. There used to be a whole series of warped French numbers used in English. That’s how we got deuce from deux, trey from trois (centuries ago, trois was pronounced like trey), cater from quatre, etc.
There was a family who lived cater-corner from me. I never got to know them and never even found out their name. So I named them the Caters. Ma Cater, Pa Cater, and the Cater tots.
I’m 67, and all I heard was “kitty-corner” (or just plain “diagonal”).
I don’t know why people cite the spelling of the word as if that settles how it’s pronounced (or as a testament to how lettered one is). There are plenty of words pronounced vastly differently from how they’re spelled. Your very citation of “deuce” and “trey,” originally Anglicized pronunciations of the words spelled “deux” and “trois,” are examples of standard pronunciations differing from spelling. As you no doubt know, the written words “deuce” and “trey” came after those novel pronunciations of the original French.
I mean, you don’t pronounce it “boat-swain” or “bee-ow-champ,” do you?
I’d say “on an angle, in the corner.”
Actually, I probably wouldn’t even say that, and more likely just point.
I’ve never used the kitty, catty, cater, whatever corner. Not a phrase I heard in my part of the world.
I would say “kitty-corner” for diagonally-opposite if I used any of the terms at all. Southern Ontario. I am wondering whether this isoneof those regional-dialect things as well.
I’m not.
Like I said, I’m literate and when growing up I would just sit and read dictionaries and encyclopedias. Other kids mocked me for reading too many books instead of playing sports or whatever, but hey. Reading dictionaries, I found the pronunciation given as ['kætər]. But my earlier post was basically about the spelling, in answer to the OP which did not ask about either pronunciation or spelling specifically, only “which term do you prefer”. My vote was for “Something else entirely,” even though it isn’t entirely different from kitty and catty, which are “corruptions” of the original term, according to Wiktionary (which also casts doubt on the etymology deriving from French, which actually doesn’t matter to my usage of the word). As a linguist I wouldn’t use value-laden terms like “corruption”—with my linguist hat on, I’d call them “variants” or something value-neutral like that, or likely “folk etymologies”—but the OP is asking about my idiolect, what I as an individual prefer to say. My individual preference is not a function of my being a linguist, though it is informed by my language studies. In other words, I’m not denouncing everyone else for getting it “wrong,” but I’m firm about how I want to say it, and I can confirm that my preference is backed up by actual data.
Always catty-corner, but the few times I’ve used it in my life, nobody seems to have known what it meant. So I’ve pretty much stopped using it altogether.
I’ve never heard anyone say kitty-corner.
I’ve always said catty-corner (though I’ve always imagined it being spelled “caddy-corner,” for some reason). I’ve never heard kitty-corner.
I grew up hearing cattycorner, and that’s what I use; kittycorner makes more sense. Catercorner neither makes sense nor is anything I’ve actually heard anyone else use, but have only seen in print.
This one is me.
Must be regional. I’m 50, been in Chicago most of those years.
Kitty-corner. Never heard the others till now.
I say catty-corner, and then my wife corrects me that it’s kitty-corner. 
Backing up Sunspace, whether you say kitty, catty, or cater, the term does not apply to the arrangement given in the OP. Maybe if you had a couch long enough to reach corner to corner diagonally across the room.
I used to work as a mover for a few years when I was in undergrad, so I used to hear this all the time. As mentioned, the proper phrase is catercorner, but I would often heard it pronounced similar to cata-corner or catty-corner. I have never heard kitty-corner, and I can only guess that it’s a play on catty-corner which is itself a mistake on catercorner.
FTR, I live in Northern Virginia.
Same here, except I use kitty-corner rather than cattycorner. Kitty-corner is intentionally diagonal, catawumpus denotes disarray.
Age 39, Chicago.
I say kitty corner but if someone said cattycorner or catercorner, I’d know what they mean. If someone said cattywumpus, I’d look at them curiously because if something is cattywumpus, it needs to be straightened immediately.
And if they said the building is catawampus from the post office, I’d assume it was about to topple into the street. 
Here’s a thought:
I did a Google image search on kitty corner to see what kind of pictures show up.
Result: One showing buildings across an intersection, One showing a piece of furniture designed to fit into a corner, and pages of cat-related pics. Oh, and a scattering of human females in scanty attire.
I did a Google image search on catty corner to see what kind of pictures show up.
Result: A whole bunch showing building (or lamp posts or whatever) across an intersection, and a bunch of cat litter boxes shaped like a quarter circle to fit into a corner.
I did “kitty corner” (with quotes) and got a stuffed cat with a gun shoved up its ass and a HO scale strip club for your model trains :dubious: