The criticisms about XTS make sense in a context when attackers can observe successive versions of the encrypted disk (i.e. the attacker steals your laptop, makes an image of the whole disk, then puts the laptop back in your bag, and you did not notice anything; and he does it again tomorrow, and the day after tomorrow, and so on...). With XTS, every 16-byte block gets encrypted by itself, so the attacker may notice when two successive versions of the same encrypted block (the same 16-byte block within the same sector of the harddisk) contain the same data. This potentially allows for traffic analysis. If the attacker goes active, then he can put back an old version of any block, and can do so for all blocks independently.
With CBC+ESSIV, each sector has its own IV, so our recurring attacker can notice when a new version of a sector begins with the same sequence of blocks as a previous version. CBC is such that if two plaintext blocks differ at some point in a sector, the remaining blocks in that sector will diverge. In that sense, compared to XTS, the attacker's abilities for traffic analysis of CBC+ESSIV are reduced. For instance, if two versions of a given sector use the same plaintext value for the 13th block, this will be apparent with XTS, not so with CBC (unless the versions for the 12 previous sectors are also unchanged).
On the other hand, an active attacker is often happier with CBC, because he can alter bits at will within a block (provided that he does not mind replacing the previous block with uncontrollable random junk).
So no, dm-crypt does not have the exact same vulnerabilities as TrueCrypt. The envisioned scenarios (repeated eavesdropping of the same disk, hostile alterations...) are not the primary goal of full-disk encryption; really, FDE was meant for the "stolen laptop" situation, in which you don't get it back, ever. Neither solution behaves well against a more industrious attacker, but they don't fail in exactly the same ways.