PCIe and DMI = almost the same thing
QPI = entirely different protocol
Both are high speed differential serial interfaces, but beyond that they are quite different. I understand why it might look like this to the end user, but trust me: having read the internal specs, they are NOT the same.
That said, it doesn't change the answer to the original poster: DMI vs QPI is entirely a false dichotomy. Both 1156 and 1366 platforms have QPI and DMI, QPI is just "hidden" on socket 1156 and Intel marketing on its website makes it a bit convoluted to figure this out because they set up "QPI" and "DMI" as in contention, when they're complementary.
But as lemlo has discovered, some overclocking BIOSes for 1156 have options to tweak the QPI data rate of this hidden interface beyond the spec'd value, thus changing the bandwidth between the cores and the PCIe/memory interface.
Architecturally, 1156 and 1366 (uniprocessor, anyway) are extremely similar. Both have CPU cores which communicate to northbridges with QPI and northbridges which communicate to DDR3, PCIe, and southbridges (through DMI). It's just on 1156, the entire "northbridge" has been made part of the die (in Lynnfield) or package (in Clarkdale) while on 1366 only the DDR3 has moved to the CPU die; the remainder of the 1366 "northbridge" functionality remains on the X58.
The only major differences between the two platforms is 1) 1156 has two channels of DDR3, 1366 has three, and 2) the QPI on 1366 carries more data, allowing more PCIe channels on X58.
That's the difference people should be using to decide between 1366 and 1156 (or 1155, for that matter): do they need the extra 16 PCIe lanes, or the extra memory bandwidth? If not, go with the cheaper platform.