They're all tough markets, all the well known literary journals, anyway. And Tin House is a primo market, so why wouldn't it be tough? It's right up there with McSweeney's and Glimmer Train. Not to mention a lot of other toughies:
North American Review, American Literary Review, New Letters, Other Voices, Ploughshares, Prairie Schooner, Cimarron, Iowa Review, Indiana Review, Shenandoah, Georgia Review, Carolina Quarterly, Epoch, Kenyon Review, New England Review, and the list goes on and on. TriQuarterly, StoryQuarterly...
They're tough because there are a lot of people in MFA programs who are getting to write full time for a couple of years and who are really pushing themselves to write well-polished stuff. And to develop a book-length body of work. Which means that almost any MFA student probably has 5-12 stories in submission to any number of journals at any given time. Not to mention all the professors who are teaching in those MFA programs and who are submitting to the same journals.
To get a good sense of the top markets, look in the back of the latest issue of Best American Short Fiction (or is it Stories?), The Pushcart Prize, or the O Henry Awards. They'll list the magazines where the candidate stories came from. Those are the country's most prestigious journals.