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Ehh, just as competitive as any other field. As for Stanford, it depends on region. Zipperstein may be a cultural historian, but Rodrigue is much more a social historian (though you better know Ladino and Turkish or Greek if you want to work with him). The real decision to make is whether you want to be housed in a history department or a Judaic Studies program. They have different orientations and values, in the PhD training and on the job market. Either way, you'll need to be rooted in a region: Israel, Europe, North Africa, Ottoman Empire, Latin America, US, etc. No one is a Jewish historian without a region, and a good historian is going to be conversant in both settings, languages, and literatures (e.g. Leora Auslander and Maud Mandel in French Jewish history, Ken Moss and Jeffrey Veidlinger in Eastern European Jewish history, etc). Be wary of parochial programs that let you specialize in Jewish history without a solid grounding in the region's history.

Plenty of people in history work with students whose interests aren't exactly the same as theirs. Countryman is not primarily a cultural historian. He's a social movements historian and has a number of students working on urban history and the carceral state -- most also work with Matt Lassiter, some also work with Howard Brick, the more culturally-inclined work with Jay Cook, the more diasporically-inclined with Kevin Gaines, the more legally-inclined with Bill Novak, and the more gender-oriented with Sherrie Reynolds. There's also an entire urban planning school and public policy school from whom to draw committee members. Sugrue has a lot of students, but is a great advisor. There used to be a lot of Katz-Sugrue students, less so now, which may mean Katz is heading toward retirement. But it's a department filled with solid people in Af-Am history including Barbara Savage, who is simply delightful. You might think about Temple. Heather Thompson is there (though the rumor mill has her gunning for Michigan). The point is: think broadly. Urban/Af-Am/Incarceration encompasses a lot, and there are many good places to do solid work in those fields.