Con: You're already level 55
Death knights have a pretty huge advantage over other classes in that a death knight alt is immediately at level 55 thanks to the whole hero class thing. That means you spend less time grinding on the old world. With that in mind, if you have another class to level, it becomes more tempting to let that one be the boost so you spend less time leveling overall.
Con: It's pretty easy to level
Death Knights aren't as overpowered as they once were, but they still have some pretty solid skills that make leveling a breeze. If you level as frost, you have Howling Blast that allows you to tear through packs of leveling mobs like tissue paper. Just choose Death Siphon as your self-heal talent for when you get in over your head, and you're good to go. If you level as blood, you will probably never die unless you actively try to, and with the right heirloom gear and judicious use of Death Strike and Death Siphon, may even be able to solo same level dungeons. As for unholy, I wouldn't level as unholy, personally, but 2 out of 3 ain't bad.
Pro: It's sometimes annoying to level
While it is pretty easy to level as a death knight, we have mechanics problems that can make it annoying. Certainly, death knights aren't the only class that has to wait until the 70s or 80s for key parts of their endgame toolkit, but the stuff we're missing can make leveling through the 60s and early 70s an absolute drag.
Rune regeneration is the biggest culprit. Since you can't get one of those talents until level 75, you're stuck with 20 levels where you can legitimately run out of resources through no fault of your own, stuck auto-attacking for multiple seconds while you pray for a rune to refresh. One of the reasons I don't recommend you level as unholy is because Festering Strike, the strike that makes Scourge Strike non-awkward to use due to its one unholy rune cost, doesn't even come your way until level 62. Improved Blood Presence, which allows you to tank dungeons without getting critically struck, doesn't come into play until level 64. Blood Shield, which allows you to make a damage shield to save you from big hits, doesn't come your way until level 80.
In short, death knights have enough cool tools that they're still OK to level, but the tools they are missing can be frustrating, and boosting to level 90 allows you to get them right away. That said, we can always hope that Blizzard makes some fixes to these issues in patch 6.0, in which case this may be a non-issue after all, assuming you're willing to wait another patch.
Pro: The slog is ahead of you
Sure, you're level 55, but all that means is you've skipped most of the new, rebalanced vanilla questing, and now you're stuck getting through Burning Crusade, Wrath of the Lich King, and Cataclysm, all of which have not been truly rebalanced since their expansions become non-current. The expansions are, to be frank, showing their age, and 55-90 is gonna be more of a sludge than 1-55.
Now, as a vanilla-era WoW player, I enjoyed BC and Wrath when they first came out. I still like Burning Crusade better than Mists of Pandaria. That said, when you're running your 5th or 6th character through those expansions, the age shows. The textures are lower. The quests are less refined. Travel can be more annoying. Quests are not as refined and engaging as in the redesigned zones. Personally, I still love BC enough to level all my characters through it, but the last 3 characters of mine to get through the 70s all did it via Alterac Valley, pet battles, and gathering skills, because questing through was too much of a pain to bother. If you take the 90 boost, you can skip all that and be ready for the good stuff.
Pro: Veterans rewards the easy way
When the 90 boosts were first data mined, the possibility of the veteran reward came up: level 60+ characters will also get their professions increased to max level. If you're thinking of using the level 90 boost for a professions mule of some sort, death knights are the perfect choice. Since they're already level 55, you just need 5 levels, 3 or 4 of which you should get just in the death knight starting zone alone, especially with heirlooms. Of course, this assumes that veteran boost stays in and works for any level 60 character, since it could change from the test server.
Learn the ropes of endgame play with WoW Insider's DK 101 guide. Make yourself invaluable to your raid group with Mind Freeze and other interrupts, gear up with pre-heroic DPS gear or pre-heroic tank gear, and plot your path to tier 11/valor point DPS gear.