Efficiency in the sense of "comparing block cipher modes" is not the reason XTS loses integrity and resistance to chosen-ciphertext attacks. Format constraints are the major reason. To wit: there's no good place to stick an auth tag, and for that matter, no good sense of what you'd be authenticating, because you're dealing with fragments of files, not actual files.
Integrity does factor into the security model of XTS. Rogaway points this out when he explains why NIST apparently rejected CBC (the chaining gives attackers a forward bit-flipping capability) and CTR (which was rejected because it's trivially malleable). NIST claimed that some notion of resisting ciphertext tampering was part of the goal, but, as he said, and Ferguson said, and I said repeatedly in this article, nobody really knows what that tamper-resistance is supposed to mean. Attackers can tamper with ciphertext in XTS, and they can probably do it in ways that will create backdoors in binaries!
But lack of integrity checking isn't the only problem with XTS. Another problem is that XTS is for the most part the ECB mode application of XEX. You can't even get a strong definition of confidentiality from this construction, because an attacker observing block offsets into a given sector can collect useful information as those blocks are changed, changed again, changed back, and changed again. This is the attack Ferguson points out in his objection to NIST standardizing XTS, and it's also related to Rogaway's objection that NIST standardized a wide-block-narrow-block construction rather than something that behaved more like a tweakable native wide block construction. The native wide block construction would effectively randomize the whole sector, not 16-byte chunks of sectors. That would also lessen the harm from XTS's malleability, but here we're more concerned with the granularity of the data we leak by encrypting deterministically.
If you want to call the attack I'm talking about something other than "Evil Maid", that's fine by me. I'd also accept "Mary Poppins is a governess and not a maid" as a valid objection. The point is that virtual disks stored on Dropbox are exposed to far more interesting attacks than physical disk media is, because with physical media, attackers don't get an unbounded number of use-tamper-use cycles.