I’m not sure, and I’m not sure if Starwood or W have made up their minds yet either (as there appears to be different font, size, and spacing between the W and the lower case xyz). In any event, Starwood has registered both XYZ and WXYZ as standard character service marks.
The Mpls reviews appear to be generally quite good and confirm the promised hipness. Given my previous "confession of a lamer," in admitting to being "out of touch with modern fads or trends," I haven’t had an occasion to step foot inside XYZ or WXYZ, at least yet.
The San Francisco W clearly shows use of XYZ alone, but at Aloft in Minneapolis (and perhaps other Aloft locations), given the minimal spacing shown above on exterior signage and the definite compression of letters shown below, it appears both the three and four letter versions actually are in use.
As I understand it, W, one of the most well-known single-letter brands (and the only single-letter with three syllables), spawned the XYZ and WXYZ brands just over a decade ago. Starwood and W must have wanted to get the concept just right before making the debut in Minneapolis!
Can you think of a better single-letter brand than W?